||Let A be an abelian variety de¯ned over a ¯nite ¯eld. In this paper,we discuss the relationship between the p-rank of A,r(A), and its endomorphism algebra, End0(A). As is well known, End0(A) determines r(A) when A is an elliptic curve. We show that, under some conditions, the value of r(A) and the structure of End0(A) are related. For example, if the center of End0(A) is an abelian extension of Q, then A is ordinary if and only if End0(A) is a commutative ¯eld. Nevertheless, we give an example in dimension 3 which shows that the algebra End0(A) does not determine the value r(A).