Many thought, somewhat naively, that in the new century Holocaust memory would finally remain unchallenged. The opposite has happened, however: The manipulation of Holocaust history by the Jews' enemies is expanding, and so is the number of this theme's mutations. The best-known Holocaust distorter is Iranian President Mahmoud Ahmadinejad. Even worse, among his many criminal statements are calls for the elimination of Israel, which is tantamount to the promotion of a second Holocaust. A great variety of Holocaust memory falsifications has permeated not only the narrative of the Arab and Muslim world, but often also that of the West, including its mainstream. The perpetrators' motives vary. The many assaults on Holocaust memory can best be analyzed by characterizing the phenomenon according to categories. A FIRST grouping is Holocaust promotion, encouraging the extermination of the Jews, either in Israel or everywhere. Some neo-Nazi groups claim that Hitler's work must be finished. Mainly in the Muslim world, it is the logical outcome of genocidal policies. Another manipulation is Holocaust justification. It consists of "explaining" that the Jews were guilty of their own destruction by Hitler during World War II. Prominent in several non-Nazi circles, it has returned today among those promoting the destruction of the State of Israel. Holocaust denial concerns the refutation of the main facts of the extermination of the Jews. This distortion started almost immediately after the war in France, and is much more widespread than among the marginal participants in the Teheran Holocaust conference. For instance, an Italian poll conducted in the fall of 2003 showed that 10 percent of Italians think Jews lie when they maintain that the Nazis murdered millions of Jews. HOLOCAUST depreciation - the next category - refers to the belittling of the severity of the Holocaust. It sometimes overlaps with Holocaust denial. In France it is often linked to the National Front and its leader Jean Marie Le Pen. In 2003 a poll of 2,000 young Italians aged 14-18, under the auspices of Italy's president, Carlo Azeglio Ciampi, showed that more than 17 percent believed reports of the extermination of Jews during the Holocaust were "exaggerated." Yet another category is Holocaust equivalence, alleging that the Germans' murderous behavior was similar to the actions of the Allies. Nowadays one finds such accusations frequently against the US, often concerning the war in Iraq. Among its many perpetrators are voices from the Western extreme Left. Holocaust inversion targets mainly Israel and Israelis, though the perpetrators sometimes mention Jews as well. It claims that the Israelis have become the Nazis of today. This rabid anti-Semitic concept appeared in the European mainstream decades ago. Back in the early 1980s, leading European socialist politicians such as French president Fran ois Mitterrand, Swedish prime minister Olaf Palme and Greek prime minister Andreas Papandreou were accusing Israel of using Nazi methods. Holocaust inversion has made major inroads in the Western world. In Germany, the 2004 German Marshall Fund poll interviewed 2,656 people in the country. Sixty-eight percent agreed that "Israel is carrying out a war of destruction against the Palestinians." Fifty-one percent agreed that "What the State of Israel does today to the Palestinians is in principle not different from what the Nazis did in the Third Reich to the Jews." PORTRAYING ISRAEL as a Nazi state enables its enemies to kill three birds with one stone. The first is to delegitimize Israel by associating it with the symbol of evil par excellence. Second, one can attack and humiliate the Jewish people by equating it with the perpetrators of the brutal genocide that exterminated most of the European Jews. Finally, the malicious analogy between Israelis and Nazis frees Europeans of remorse or shame for their history of a lethal anti-Semitism lasting many centuries. YET ANOTHER category is the trivialization of Holocaust memory in recent years. This manifests itself in applications of language relating the industrialized murder of the Jews to other matters - transgressions of international law, environmental problems, abortion and animal slaughter - which bear no similarity to this genocide. A related manipulation is the attempt to silence Holocaust memory by accusing the Jews of mentioning the Holocaust too often. The aforementioned 2004 poll found that 62% of the Germans were fed up with hearing about their country's crimes against the Jews. In its extreme form, this category includes attacks on Holocaust memory, and even attempts to destroy or damage Holocaust memorials. What can be done? The manipulation of Holocaust memory is a symptom of a much larger problem in society, of which anti-Semitism is a major, but far from the only, aspect. Fighting Holocaust distortion is a complex process, one for which no coherent strategies exist at present. It is therefore important to first gain a much better understanding of each of the abovementioned categories, identify who is using them, and investigate how the perpetrators can be counteracted or punished. The writer, chairman of the board of fellows of the Jerusalem Center for Public Affairs, is writing a book on Holocaust distortions, sponsored by the Rabbi Israel Miller Fund for Shoah Research, Documentation and Education of the Conference on Jewish Material Claims Against Germany.