Recently, a D-brane construction in type IIA string theory was shown to yield the electric/magnetic duality of four-dimensional N = 1 supersymmetric U(N-c) gauge theories with N-f flavours of quark. We present here an extension of that construction which yields the electric/magnetic duality for the SO(N-c) and USp(N-c) gauge theories with N-f quarks, by adding an orientifold plane which is consistent with the supersymmetry. Due to the intersection of the orientifold plane with the NS-NS fivebranes already present, new features arise which are crucial in determining the correct final structure of the dualities. (C) 1997 Elsevier Science B.V.