We discuss the formation of secondary synchronized clusters, that is, small clusters of synchronized oscillators besides the main cluster, in second-order oscillator networks and the role of inertia in this process. Such secondary synchronized clusters give rise to non-stationary states such as oscillatory and standing wave states. After describing the formation of such clusters through numerical simulations, we use a time-periodic mean field ansatz to obtain a qualitative understanding of the formation of non-stationary states. Finally, the effect of inertia in the formation of secondary synchronized clusters is analyzed through a minimal model. The analysis shows that the effect of the main synchronized cluster on the other oscillators is weakened by inertias, thus leading to secondary synchronized clusters during the transition to synchronization.