All following considerations are independent of dynamics. Four simple theorems are proven concerning experiments which can determine intrinsic parities of particles or experiments which can test the validity of invariance under space reflection, time reversal, and (assuming theCPT theorem) charge conjugation. The last two of these invariance principles are discussed only for elastic reactions. It is shown, among other things, that both parity determination and testing of invariance principles are essentially impossible in reactions involving more than four particles, and are possible in four-particle reactions essentially only if some spin information is obtained about all participating particles.