The American GI, the legendary free spender of the postwar era overseas, has run into hard times here in West Germany, a country that until recently was a choice assignment for young soldiers.

The reason is the dramatic nose-dive of the U.S. dollar, which has lost almost 20 percent of its value against the powerful West German mark in the past year.

To a GI, it means that a beer at the "Top Ten" disco for a single and lonely soldier now costs $1.10, more than twice what is costs at the enlisted mens' club on the big U.S. 3rd Infantry Division base here. It means an occasional break from the routine of mess-hall eating for a single hamburger in town costs the equivalent of $1.80.

It means that a family that is not eligible for government quarters and that pays 350 marks a month rent now must cash in $180 to pay the rent instead of $150 just six months ago.

It means a few meatless days a month for many young families living off the base and it means - potentially at least - trouble for the Army's combat efficency and reenlistment rate if things get worse.

The situation has produced bewilderment about the lofty international monetary affairs that produce such effects and some bitterness directed toward the U.S. government.

But stories about Germans sending food parcels to needy families, of soldiers living worse here than they would on welfare in the United States, and of chairs being tossed out of windows to relieve the financial frustration, appear to be exaggerations in most cases.

Interviews here with a dozen soldiers and some of their wives indicate that things are tough, especially for the lower-ranking married GIs. But most say they have been able to adjust thus far and additional army housing and cost-of-living allowances going into effect this month should help.

"It's tough, but it's something you live with," says Catherine Cochrum, the wife of 21-year-old Cpl. Elton Cochrum. "We don't walk around depressed and bad-mouthing the Army," he adds.

"I don't think I could bring myself to ask the landlady to lower our rent," says 19-year-old Cpl. Rady Woods. "It's not the Germans' fault that the dollar is going down. It's the U.S. government's fault."

Woods, his wife and baby live in a neat but tiny three-room basement apartment in a German village, near the Cochrums and a few miles from the base.

Because Woods and Cochrum are still low in rank and have served less than two years, they do not qualify for free government housing for their families and they also have to pay to transport their dependents and their household goods overseas out of their own pockets.

These two so-called "non-command sponsored" families - along with some 16,000 other low-ranking GI families in the same boat in Germany - are the hardest hit of the 190,000 U.S. soldiers and 200,000 dependents in this country.

They joined the volunteer Army on the shortest available three-year enlistment and the Army doesn't want to invest in the expense of shipping dependents and furniture overseas for what may be a short-time solider.

But the dropping dollar now means that a corporal in this category may have to use perhaps one-third or more of his $735 monthly take-home pay to buy German marks to pay his rent and utilities. If he can't afford a car, his wife usually has to take a taxi home from the commissary with the groceries or to and from the base laundry.

It is this group that the army has focused on and is trying help with new allowances that average about $30 monthly and by opening up mess halls to dependents so that a family of three can have a full course meal now for $3.50 combined.

It is this group that has also gotten most of the publicity. Yet they are a small percentage of the troops over here. Officials point out that actually 4,000 of those 16,000 families are sergeants, whose salaries provide much more leeway.

Salaries at all ranks have sharply increased under the all-volunteer Army in recent years and all soldiers, including those who live off base, are protected by post exchange system whose managers here say sells products at 20-50 percent less than U.S. retail prices, a food commissary with prices roughly 20 percent below U.S. prices and a gas station that pumps out high-test at 65 cents a gallon.

The most severe problem for the Army actually may turn out to be not the solid young families but the tens of thousands of single GIs who jam the stereo equipment section of the PXs around Germany. They like to get off the base as often as possible and, in perhaps 5 or 10 percent of the cases, also want to live off base.

There is no way, however, for the Army to provide allowances for soldiers who, on paper, have their every need, including a bed, provided by the Army.

Yet it is here that most of the bitterness is directed, perhaps unfairly, at the Army.

"The Army screwed me," is the way an 18-year-old private from Michigan put it. "Back home at least I had some money in my pocket. But here I just sit with no money, no place to go. You can't lock the damn doors in the barracks. You can't sleep because guys are always coming in and out. There's no privacy and now I'm in debt because I signed a lease on an apartment in town and my roommate moved back to the base because he can't afford it either."

Another GI claims that one-fourth of is platoon has tried to live off base just on the basic salary. More GIs are using their cigarette and whiskey rations from the PX on the German black market where they can sell them for more than double the purchase price.

The statistics in the community relations section of this base show the alarm signals. Since last fall, 70 out of 83 families receiving marriage counseling reported financial problems. Red Cross and Army emergency relief loans are climbing, but the numbers involved are still very small for a community of 10,000 persons.

Last fail, before the new allowances came into effect, 40 GIs sent their dependents back to the United States from here. And at year's end, the base commander, in his annual message to roughly 900 German landlords who rent to GIs in this blue-collar town in central Germany, discreetly inquired about prospects for lowering the rents.

Only a handful have repsonded positively, but Pvt. Lee Edwards, who lives off bass with his wife and baby, says his landlady voluntarily cut his rent. Cpl. Woods says he thinks his landlady is charging less now for utilities than they really cost, so that there are individual acts of kindness being displayed.

But Lt. Col. Albert Spaulding, a former battalion commander who now watches over community affairs, says "I personally can't support begging the Germans when our government has made the basic economic decision to let the dollar float" on currency markets, which has pushed it down.

"If the U.S. decides on an economic policy, it ought to say 'okay, here's what we do for the Army.' If we are committed to be here for strategic or policy reasons, then it's up to the government to support that. If there is a financial problem, it shouldn't be borne by Cpl. Smith.

"And if the Germans want us to take part then it should come from the German government and not Herr Smidt," he adds, referring to the average German.

"There's no question, Spaulding says of the hard-pressed soliders, "that these guys are not able to provide those things above the basic necessities.

"So if you say 'Yeah, I'm sleeping, eating and getting to work and not doing anything else,' and you take the point of view that a soldier just needs to survive, then he doesn't need anything else."