Just to be precise with wording...
- Nazism - the political principles of the National Socialist German Workers' Party.
So this principle is not bound to to Germany. Neo-nazi's are spread around the world, if I'm not wrong. - Nazi - a member of the National Socialist German Workers' Party.
- Fascism - a political philosophy, movement, or regime (such as that of the Fascisti) that exalts nation and often race above the individual and that stands for a centralized autocratic government headed by a dictatorial leader, severe economic and social regimentation, and forcible suppression of opposition.
- Racism - prejudice, discrimination, or antagonism directed against someone of a different race based on the belief that one's own race is superior.
One shouldn't confuse Nazism and Fascism.
As I understand, Nazism means defending the national interests (support), doing some efforts to make nation better (this could be done in bad and good ways, though).
Fascism means dictatorship and extermination of any opposing minds. On genetic and cultural levels this make nation weaker, but gains the power and influence of dictator.
When dictator voluntarily makes nation weaker in some aspects by Fascism, he needs to suppress other nations. Otherwise its nation will quickly become non-competitive. This is why Racism goes together with Fascism.