A systematic numerical analysis is performed for superharmonic excitations in a wake where a circular cylinder is rotationally oscillated in time. Emphasis is placed on identifying the secondary and tertiary lock-on in the forced wakes. The frequency responses are scrutinized by measuring the lift coefficient (CL). A direct numerical simulation has been conducted to portray the unsteady dynamics of wake flows behind a circular cylinder. The Reynolds number based on the diameter is Re = 106, and the forcing magnitude is 0.10 [les ] Ωmax [les ] 0.40. The tertiary lock-on is observed, where the shedding frequency (St0) is one third of the forcing frequency (Sf), i.e. the 1/3 subharmonic lock-on. The phase shift of CL with respect to the forcing frequency is observed. It is similar to that of the primary lock-on. However, in the secondary superharmonic excitation, modulated oscillations are observed, i.e. the lock-on does not exist. As Ωmax increases, St0 is gradually shifted from the natural shedding frequency (St*0) to lower values. The magnitudes and phases of Sf and St0 are analysed by the phase diagram. The vorticity contours are employed to examine the vortex formation mode against the forcing conditions.