Two identical circular cylinders are submerged to the same depth in tandem in a stream. There are separation distances between the cylinder centres such that the combination makes no downstream waves, and hence is subject to zero net wave drag. In general there is then a non-zero equal and opposite horizontal force on each cylinder. However, there are special depths of submergence such that this interaction force between the cylinders also vanishes, and hence each cylinder is separately free of horizontal force. The parameter range for this phenomenon is explored both by linear theory for cylinders of small radius, and by a fully nonlinear computer program. For example, a configuration with a separation distance of approximately one half-wavelength gives zero force on each cylinder when the depth of submergence is approximately three-quarters of the separation distance.