The steady magnetohydrodynamic flow of a conducting, incompressible Oldroyd-B fluid due to noncoaxial rotations of a porous, insulated disk and the fluid at infinity with the same angular velocity is considered. It is shown that the problem has a solution for the suction case but it admits no such a solution for the blowing case. The velocity field and the shear stresses are calculated according to the suction parameter e(0), the Deborah number D, the elastic number alpha and the magnetic parameter N. It is observed that the magnetic parameter N makes g(z) function, which gives a translational motion to gamma-component of the velocity field, negative in the range of certain small values of e(0), D and alpha. Separately, it is found that there is no solution at some values of e(0) and D for a Maxwell fluid which is a subclass of an Oldroyd-B fluid. (C) 2000 Elsevier Science Ltd. All rights reserved.