The notion of anaphoric conservativity, that is a property of specific functions taking sets and binary relations as arguments is studied. Such functions are denotations of anaphoric determiners forming nominal anaphors. It is shown that anaphoric conservativity is strictly stronger that ordinary conservativity of this type of functions. In consequence some novel semantic descriptions of reflexive and reciprocal pronouns are provided and a semantic universal stating that reflexive and reciprocal non-possessive determiners denote anaphorically conservative functions is proposed.