Summary: We consider the oscillating flow about a pair of circular cylinders of unequal diameter. In addition to the relative size of the cylinders, the distance between them can be varied, as can the angle that the undisturbed oscillatory flow makes with the line joining the cylinder centres. For small-amplitude vibrations a time-independent, or steady streaming, motion develops that persists beyond the Stokes layer that forms at the solid boundary. This persistent streaming is considered for large values of a suitably defined streaming Reynolds number.