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Let p be a prime, e a positive integer, q = pe, and ��q denote the finite field of q elements. Let fi : ��2q → ��q be arbitrary functions, where 1 ≤ i ≤1, i and l are integers. The digraph D = D(q:f), where f = f ,..., f l): ��2q → ��lq, is defined as follows. The vertex of D is ��l+1q. There is an arc from a vertex x = (x1,...xl+1) to a vertex y = (y1,...yl+1) if xi + yi = f i-l(x1, y1) for all i, 2 ≤ il + 1. In this paper we study the strong connectivity of D and completely describe its strong components. The digraphs D are directed analogues of some algebraically defined graphs, which have been studied extensively and have many applications.