Mengele: THE COMPLETE STORY by Gerald L. Posner and John Ware (McGraw-Hill: $18.95; 330 pp.,illustrated)

This is not, as the subtitle claims, “the complete story” of Dr. Josef Mengele, the Nazi “Angel of Death” who caused the death and suffering of tens of thousands of inmates of the Auschwitz concentration camp. Nor could it be, for the key witness is missing.

The witness is Mengele himself. For 35 years after World War II until he died of a stroke in 1979 at the age of 67 while at a beach near Sao Paulo, Brazil, Mengele eluded capture as the most wanted Nazi war criminal. The world did not learn of his death until six years later, and had never confronted him about his crimes. As one of Mengele’s Israeli pursuers had put it: “We wanted him to stand trial so that the world could see what a monster he was.”

The book deals only briefly with the 21 months Mengele served at Auschwitz. Utilizing what they say is a unique collection of documents, including letters and other writings by Mengele, the authors concentrate on what is a fascinating account of Mengele’s life on the run and the fruitless efforts to apprehend him.

That Mengele was able to elude justice was not the result of his skills at evasion or to the network of family, friends and venal opportunists that had helped him. It was mainly due, the authors say, to a “real travesty”--the half-hearted, ineffective efforts of American, Israeli and West German authorities to press the hunt. The authors show with convincing arguments that Mengele was able to maintain his freedom thanks to governmental bungling, indifference, political expediency, bureaucratic obstacles, corrupt Latin officials and unrepentant Nazis.

They also place a large share of the blame on Nazi-hunters Simon Wiesenthal, Serge and Beate Klarsfeld and Tuvia Friedman. The authors maintain that in their well-intentioned zeal to apprehend Mengele, the Nazi-hunters actually hindered the search by littering the trail with what turned out to be false claims that Mengele’s hideout in Argentina, Paraguay or Brazil had been spotted and that he was about to be caught, claims made even long after he had died.

Posner and Ware have found no heroes in what became a long, sad postscript to the agonies of Auschwitz.