The degradation of the surface impedance Z=R + iX with rf power is a p
rincipal limit for measurements and applications. Such nonlinearities
occur for normal conducting cavities by heating or electron loading. B
ut superconductors show a much richer spectrum of causes for nonlinear
ities. The nonlinearities in the surface resistance delta R proportion
al to gamma H-n and surface reactance delta X proportional to alpha H-
n can be classified by the ratio r=delta X/delta R. This ratio differs
in value, temperature, or frequency dependence for the different mech
anisms, allowing a unique identification of those mechanisms. This ide
ntification is a prerequisite for an improved rf cavity design and imp
rovement of superconducting materials.