The directed circulant graph Cn(1, 2, … , t) consists of the vertices v0 , v1 , … , vn-1 and edges directed from vi to vi+j for every i = 0, 1, … , n – 1, and j = 1, 2, … , t, where 1 ≤ t ≤ n – 1, the indices are taken modulo n. We present lower and upper bounds on the partition dimension of very general graphs Cn(1, 2, … , t). Our bounds yield exact values of the partition dimension of the graphs Cn(1, 2, … , t) for t = 2, 3, 4 and n ≥ 10.