In the ideal middle stages of a multi-stage axial-flow turbine, we take, as one stage, any adjoining two rows of blades such as I, II which are moving to the opposite directions with each other. The adiabatic heat drops of the moving blades I and II are (1-ρ) H0 and ρH0 respectively, when we represent the total heat drop of the stage with H0 and adopt a factor ρ called "ratio of heat drops". For the blades I and II, we take c', c as circumferential velocities, ζ', ζ as coefficients of loss and β2', β2 as exit angles, respectively. We represent the relative velocity of fluid at the exit of the blades II with u2. Taking the velocity ratio ξ2= (c'+c)/u2 and the function about energy ratio Au22/(2gH0)=Φ, the circumferential efficiency ηc of an ideal middle stage may be given by the next equation [numerical formula] if we have the suitable value of the angle β2', calculated from the following equation [numerical formula] Using these equations, we have made clear numerically the performance of double-rotation axialflow turbines. And comparing these turbines with double-rotation radial-flow turbines, we have confirmed again our old deduction. In general we may expect to realize more efficient doublerotation turbines, if we are able to get the combinations of two blades having the sections suited to the given theoretical condition, not being restrained for any stage by such construction with two rows of blades having same sections as in Ljungstrom turbine.