In this talk, we introduce several models of the so-called forward-forward Mean-Field Games (MFGs). These models arise, for example, in the study of numerical schemes to approximate stationary states of MFGs. We establish a link between the forward-forward Mean-Field Games and a class of hyper- bolic conservation laws. Furthermore, we show how these models are connected to certain nonlinear wave equations. Finally, we investigate the existence of solutions and examine their long-time limit properties. Joint work with Diogo Gomes and Levon Nurbekyan.