Silvery flying skimmed over the moonlit Caribbean waves, a picture of delight that contrasted with the sinister silhouette skipper Michael Muragh spotted through the telescope mounted on the bridge of this Coast Guard cutter.

Sliding northward along the Mexican side of the Yucatan Channel between Mexico and Cuba was a dark shape larger than its running lights were advertising.

Murtagh ordered lights out on his 210-foot cutter so it could sneak up on the suspect vessel before it might dash out of the channel's international waters and into the territorial waters of Mexico where the U.S. Coast Guard cannot pursue. The Yucatan Channel is a main thoroughfare for smuggling marijuana and hard drugs by sea from Colombia to the United States. The USS Dauntless, on this moonlit February night, was on patrol.

Because smugglers recently have begun shooting at Coast Guard cutters rather than surrendering their multimillion-dollar cargoes of dope, Murtagh ordered the two .50-cal. machine guns on the bridge of the Dauntless loaded and two men posted there with M16 rifles.

"Got that feeling, captain?" asked Lt. Cmdr. Andrew Anderson, the Dauntless' executive officer and second in command.

"I really do," Murtagh replied. The two officers stood on the darkened bridge and studied their quarry. It was sailing outside of the main line of channel traffic 20 miles east of the Mexican port of Morelos.

The brief Caribbean drama that was to follow provided a lively illustration of what every Coast Guardsman knows: the sixth-largest seagoing force in the world is badly overextended, with more missions than it can fulfill. It can still win the occasional battle but is losing the war.

"We're in desperate straits," warns Coast Guard Commandant John B. Hayes in a plea that so far has failed to impress President Reagan's budget chiefs. The Coast Guard, that "other" service, is not receiving any of the extra billions the Reagan administration is showering on the Army, Navy, Air Force and Marine Corps. The General Accounting Office found in a recent study that ". . . the Coast Guard's responsibilities have increased without a commensurate growth in its resources."

A week aboard the Dauntless illustrates what the Coast Guard is suffering from -- problems of identity, of people, machines and money. Congress must decide soon whether to rescue the Coast Guard or redefine its role.

That was not the issue, however, as the Dauntless closed to within 1,500 yards of the suspected smuggler, still on the northward course through the Yucatan Channel, still apparently unaware of its pursuer.

Murtagh could see plainly now that the suspect was a shrimp boat, about 60 feet long and stripped of masts, nets and other standard shrimping gear. It was definitely not the small sailboat that its running lights implied.

The Dauntless swung around the shrimp boat so it could block any run for Mexican waters. There was no longer any need to play cat-and-mouse.

"Turn on our blue lights," Murtagh commanded. "Light up our flag."

With that, blue lights indicating a law enforcement mission blinked from the cutter's mast. A searchlight illuminated the U.S. and Coast Guard flags snapping in the 10-knot east wind rippling the channel's surface.

"Light him up!" Murtagh barked from his post on the starboard wing of the cutter's bridge.

A shaft of blinding light from a 2-foot-wide arc light shot across the water from the Dauntless to the shrimp boat, focusing on its transom.

The shrimper's name and home port read: "Capt. Kris, Houma, La." The bright light revealed that the waterline of the 62-foot Capt. Kris had been smeared with paint, evidently to hide the fact that the boat was heavily laden.

Some of the searchlight beams spilled off the transom of the Capt. Kris and formed a big pool of light atop the blue-black water of the channel. Flying fish soon found it and began frolicking in this play pool of light in their own back yard.

Murtagh directed Lt. Larry Yarbrough to break radio silence and raise the Capt. Kris.

"What is the purpose of your voyage, over?" Yarbrough asked after some preliminary back-and-forth on the radio.

"We were delivering this boat to Belize when we had some trouble with our outriggers, our mast, which we lost this morning. We're returning to have our rigging taken care of and finally put in shipshape order before we make delivery of this vessel, sir."

"Captain, this is the U.S. Coast Guard directing you to heave to."

"Roger on that," a crewman on the Capt. Kris replied. "We are heaving to."

Six Coast Guardsmen, all armed with .45-cal. pistols and one with a riot shotgun, formed up on the Dauntless as the boarding party. Wearing helmets and flak jackets under their life preservers, they climbed into one of the two 25-foot surfboats slung on the sides and were lowered into the water.

The surfboat's crew motored the boarding party to the side of the Capt. Kris while the machine gunners and rifelmen on the Dauntless bridge kept them covered.

Lt. Mark Fiebrandt led the party aboard, and ordered the shrimper's three-man crew to assemble on the bow while Coast Guardsmen searched the holds and pilothouse.

"Is Charlie up there?" one of the searching Coast Guardsmen radioed from the Capt. Kris to the Dauntless.

"Bingo!" Murtagh exclaimed. "Is Charlie up there" was code indicating that marijuana had been found on the vessel. The Capt. Kris was what the Coast Guard calls a "doper," and its crew was subject to arrest.

The Dauntless' boarding party found bale after bale of marijuana crammed into the shrimper. Each bale was wrapped in plastic, then burlap, complete with rope handles for easy loading. The boarding party took a rough count of the bales. An estimated 20 tons of marijuana were stashed in the Capt. Kris. That amount would bring about $16 million when sold on the street.

The crew of the Capt. Kris also had two rifles and pistols aboard, perhaps to defend against a hijacking.

The Coast Guardsmen ordered the three crewmen to lean over the bow rail, hands behind their backs for handcuffing.

"That's a sight we love to see," exulted executive officer Anderson.

The three were athletic men in their 30s who apparently had been paid only a fraction of their cargo's worth to transport the marijuana. They looked as if they had just left the international beachcombing set, wearing beards, sandals, shorts and T-shirts.

The prisoners were brought to the Dauntless by surfboat one at a time. They were ordered to strip under bright lights on the Dauntless' deck, they were searched thoroughly for hidden weapons such as razors. None was found.

"Dehumanizing," Murtagh conceded as he watched the strip-search.

After putting their sailing clothes back on, the prisoners were shackled by the legs to a thick chain along the open starboard deck. They were kept there day and night, except for trips under guard to a portable toilet, until the Dauntless returned to Miami Beach.

Charged with possession of marijuana and intent to distribute it were Johnny Lawrence McMurtrey, 38, of Mississippi; James Loren Shaw, 30, of California, and Lester Wyman Willis, 31, of Connecticut. The Coast Guard gave no home towns for the three, who were said to have wandered from place to place in recent years. Each of the accused could be jailed for as long as 15 years and be fined $25,000 under a tough antismuggling law enacted last year.

The Dauntless posted armed men on the Capt. Kris in hopes of catching a ship the Coast Guard suspected might rendezvuos to pick up the bales, but no such meeting took place. So a Coast Guard crew saled the confiscated Capt. Kris and its marijuana back to Miami Beach while the Dauntless kept the dope boat in constant sight in case of breakdown or attempted hijacking.

Shortly before reaching port, the Dauntless" crew painted its 37th marijuana leaf on the cutter's mast -- each signifying a successful drug bust -- and hoisted its marijuana flag.

Commandant Hayes acknowledges that the Coast Guard is losing its war against marijuana smugglers. He estimates that the more than $1 billion worth of the weed confiscated at sea last year represents less than 20 percent of the seagoing dope traffic.

Unless Washington gives the Coast Guard more money, cutters such as the Dauntless can win only battles against the dopers, not wars, Hayes said.

"It's Prohibition all over again," one Dauntless officer said, acknowledging that the Coast Guard's best efforts are putting only a slight crimp in the dope smuggling.

Some Coast Guardsmen on the Dauntless freely admit that they have smoked pot themselves, and wonder aloud if the U.S. government should legalize the use of marijuana to take trafficking out of the hands of racketeers, control the quality of the substances and tax sales.

"There has always been a debate within the Coast Guard whether we're firemen or cops," said the Dauntless' Murtagh.

That is the identity crisis: Should cutters and their on-board helicopters be out chasing dopers? Or looking for stranded vessels and drowning passengers? Or checking coastal waters for oil spills? Congress has ordered the Coast Guard to do all these and more.

Congress established the forerunner of the Coast Guard in 1790, when it directed ships of the Revenue Cutter Service to stop cargoes being smuggled past American tax collectors. This antismuggling responsibility was enlarged in subsequent years.

In the 1860s the Coast Guard tried to keep opium from being smuggled into California, and, in the 1930s, it fought rum-rummers trying to skirt the Prohibition amendment with high-speed boats.

Now, as Commandant Hayes has pointed out to the Reagan administration budget cutters, Congress has directed the Coast Guard to enforce 21 different laws. These include acting as game warden in the huge fishing area extending 200 miles from the American coast, catching oil and chemical polluters, policing and rescuing weekend boaters, inspecting offshore oil rigs, checking boat pilots on the Great Lakes and inspecting the way shipyards build tankers.

President Carter seemed to be acknowledging that the government was asking the Coast Guard to do too much with too little when he said, in recommending a $2.2 billion appropriation for fiscal 1982: "A major review the balance of the century is scheduled for 1981." He recommended keeping the Coast Guard at 39,900 military and 6,000 civilian personnel in the meantime.

Hayes worries that Reagan's advisers will cut the Coast Guard budget first and then study what it should do. So Hayes is stressing the Coast Guard's military contribution, as evidenced by a private memo he sent his boss, Transportation Secretary Drew Lewis.

"I am dismayed," Hayes wrote, by Reagan administration recommendations to cut the Coast Guard budget by more than what Carter had proposed. "In every major conflict in recent memory, the Coast Guard has been called upon to contribute to Department of Defense forces.

"Given the emphasis our nation is placing on defense, it is foolhardly not to grant the Coast Guard the priority treatment accorded Department of Defense in this budget review. Our problems are identical, our national security contribution is unique and our contribution to the public welfare during peacetime is unmatched by the other armed forces."

Even the Carter budget, Hayes is telling Congress, was not enough to keep the Coast Guard from becoming something less than a varsity outfit. He is recommending an immediate addition of $700 million and 2,800 more people as emergency lifelines, with more money and people needed in later years to revitalize the Coast Guard.

Hayes is taking a risk by trying to hitch the Coast Guard to his rich cousins, the Army, Navy, Air Force and Marine Corps, all of whom are under the Department of Defense while the Coast Guard is under the civilian Transporatation Department.

This emphasis will tempt Congress to dismember the Coast Guard, perhaps by putting seagoing cutters such as the Dauntless under the Navy and transferring antipollation and antidrug activities to other federal agencies.

Patrolling with the Dauntless recently illustrated one difference between today's Coast Guard and the other services: the Coast Guard draws quality people into its ranks. But the patrol also dramatized Hayes' warning that the Coast Guard is taking on water faster than it can bail in terms of skilled sailors and broken equipment.

"I joined the Coast Guard because I saw it was a way to save lives two ways," said Rick Groover, 21, of Leesburg, Fla., in an interview aboard the Dauntless. He conducts lay services on Sundays aboard the ship. "I could save lives at sea, and by keeping people from smoking the marijuana we stopped."

"I really didn't want to join the regular military," said electronics technician Toby Faulkner, 28, a first class petty officer, a rate in short supply in all the services. "The other services seemed to be waiting for a war. The Coast Guard seemed to be something different. We go out to save lives, not destroy them."

"I enjoy the job a whole lot," said Lt. William Spitler, 29, of Dover, Fla., a helicopter pilot who was training for which private airlines would pay more than does the Coast Guard. "We really pull people out of the jaws of death. It's a real good feeling. I hoisted 25 people off a dredge that was breaking up in 40-knot seas."

Commandant Hayes is afraid a ship soon may sink because the Coast Guards has nothing to send to its rescue.

The Dauntless could not leave on time to patrol because of a broken coupling in the hoist for lowering and raising the starboard surfloat. The Coast Guard, which had no replacement in stock, scoured private marinas and finally bought a coupling 40 miles from the Dauntless' berth.

"Getting under way is always a trauma," said Executive Officer Anderson.

While the Dauntless was waiting at the dock for the part, a private plane flew over it trailing this sign: "George Washington grew marijuana."

"Nobody is supposed to know we're leaving," Murtagh said. "Kind of makes you wonder, doesn't it?"

Some engineroom technicians were uneasy about one of the Dauntless' two diesel engines because it had missed a scheduled overhaul for lack of money.

The gun on the bow of the Dauntless is so old that when it needs a spare part "we go to VFW halls and museums," Anderson said.

The H62 helicopter perched on the fantail could not be sent to pursue a suspected dope ship running away from the 18-knot cutter. The 1964 helicopter had burned out a vital part that had failed several times.

A new part was airdropped on the cutter for the chopper, at a cost of about $1,000 in airplane fuel alone. But, for want of the right part at the right time, the helicopter flew only one search mission in one week at sea.

Murtagh said the Coast Guard is so short of petty officers that it is taking inexperienced sailors off ships and sending them to schools to fill this middle-management gap. This leaves the Dauntless with green sailors most of the time.

Inexperienced sailors are teen-agers who can make big mistakes at sea. One young man on the Dauntless, for instance, mistakenly cut the heaving line thrown to a sailboat in need of help.

The Coast Guard motto is "Semper Paratus" (Always Prepared) -- but the Coast Guard is sending its own district signal to Washington's decision-makers: prepared for what?