Abstract. We determine the primitive positive clones $F$ on finite sets $A$ with at least three elements for which $(A;F)$ is simple and idempotent, and the primitive positive clones $F$ having all constant operations for which $(A;F)$ either generates a congruence distributive variety or is a simple algebra that is not strongly abelian.

AMS Subject Classification (1991): 08A40

Received January 15, 2007, and in final form August 19, 2007. (Registered under 6446/2009.)