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We investigate Mal'cev conditions described by equations whose variables runsover the set of all compatible reflexive relations. Let $p \leq q$ be anequation in the language $\{\wedge, \circ,+\}$. We give a characterization ofthe class of all varieties which satisfy $p \leq q$ over the set of allcompatible reflexive relations. The aim is to find an analogon of thePixley-Wille algorithm for conditions expressed by equations over the set ofall compatible reflexive relations, and to characterize when an equation $p\leq q$ expresses the same property when considered over the congruencelattices or over the sets of all compatible reflexive relations of algebras ina variety.

Mal'cev conditions corresponding to identities for compatible reflexive relations