The Sphinx, the symbol of ancient Egypt's mystery and majesty, is suffering from one of mankind's most deadly diseases--cancer.

This, at least, is what American archeologists involved in the restoration of the 4,500-year-old limestone monument have nicknamed the salt erosion afflicting the already badly pockmarked statue--one of this country's national treasures--sitting at the foot of the Great Pyramids on the western outskirts of Cairo.

Whether the Sphinx is being treated properly or allowed to die a slow death is now at the center of an international controversy that came to public light last October when a small chunk of its left hind leg fell off.

Egyptian antiquities authorities insist that everything needed to preserve the famed statue will be done regardless of cost, including a major restoration program now in preparation.

"There is nothing too expensive for our Sphinx," Ahmed Kadri, head of the Egyptian Antiquities Organization, said. "We will spend even half of our total national budget if necessary."

Whether even those billions of dollars could save the Sphinx from Father Time is questionable. The statue--a lion's body with a human head draped in a royal headdress--is in sad shape already.

Religious fanatics, or Mameluk gunners practicing their canon aim, long ago destroyed the nose and part of the face.

Its beard has fallen down, centuries of wind erosion have made deep cuts into its sides and fissures run through its body. Finally, around the base is a mishmash of stone patches from half a dozen epochs stretching back 3,400 years.

Some American benefactors and archeologists fear that the current "temporary" repairs being carried out on the Sphinx's left front and back paw will just add more patches and that the full-scale restoration project being talked about will die a slow death in Egypt's infamous bureaucracy.

"My concern now is that the repair work will be perceived as the final solution," said James P. Allen, director of the American Research Center in Egypt, which has undertaken an archeological history and mapping of the Sphinx's stonework.

"It would be a mistake," he said.

One American benefactor, Susan Beth Franzheim, wife of a former U.S. ambassador and a director of the Franzheim Synergy Trust of Houston, was so upset by the repair work she saw going on while visiting here in March that she withdrew the foundation's money after accusing the antiquities office of bureaucratic delay and ignoring professional U.S. advice.

"She insulted us," snapped Kadri. "We are not begging anyone to give us money."

The controversy over the care being taken to restore the Sphinx centers around the stone and mortar patchwork done to its surface over the centuries, but especially since 1926 when the statue was dug out of the sand in which it had long been buried up to its neck.

American archeologists working at the site say much of the new stone and mortar is "cancerous," a term used by Prof. K. Lal Gauri from the Stone Conservation Laboratory at the University of Kentucky in Louisville.

By this they mean that the new material's salt content is so high that it is causing the flaking away not only of the new stone but also of the ancient limestone around and underneath the "cancer patches."

It effect, erosion of the stone is being spread by the modern-day repair work, an irony that one American archeologist likens to the filling in a tooth doing more damage then the original cavity.

Making matters worse, in the view of American and Egyptian experts, the whole body of the Sphinx is figuratively "sweating salt" because the extremes of temperature draw salt out.

What happens is that the salt dissolved in water comes to the surface where it dries, crystallizes and then flakes off together with the stone under it from the action of the wind.

"The whole body of the Sphinx has this cancer," said Mark Lehner, who has done a complete diagnosis of the core and various layers of outer stones added to the Sphinx since the ancient Egyptians began repairing it back in 1400 B.C.

Only the head is free of the salt "cancer" because its stone is different, Lehner explained. But, he added,"it could eventually collapse of its own weight because of the soft stone holding it up and the modern cement under the face."

Gauri reportedly has come up with a possible cure for the salt cancer that may become the basis of the Egyptian restoration project.

According to Allen and Lehner, it would work like this: the Sphinx, piece by piece, would be wrapped in an impermeable bag, the air inside would be pumped out and then water drawn through the stone by the ensuing vacuum to eliminate the salt content, or reduce it to a safe level.

This same "vacuum technology" could be used, they say, to introduce consolidating agents to harden the stone. Gauri has reportedly offered to develop the technology especially for the Sphinx.

But Egyptian archeologists are still not sure this is the best long-term answer and they are awaiting the results of a comprehensive study begun last November of all aspects of the Sphinx's various illnesses before deciding.

"Salt alone is not the problem," said Egyptian archeologist Saleh Ahmed Saleh. "In fact, it can work as a binder and give greater strength to the limestone."

The basic problem, Saleh thinks, is the high water table that lies just 12 feet below the Sphinx and provides the solution to dissolve the salt found in the stone. He favors lowering the water table before doing anything else.

Saleh also seems more philosophical than his American counterparts about the limits of modern restoration techniques to preserve the Sphinx.

"The Sphinx was born a sick child," he said in an interview at the site. "Even the ancient Egyptians were working to restore it. We will do what we can to preserve it for the next generation. The parts that have collapsed must be restored now without waiting for the studies."

But Saleh says there is just so much the Egyptians, or anyone, can do to retard the ancient Sphinx's final disintegration. "You have to leave the mark of time on your monuments," he said.