Coupled cell systems are dynamical systems which respect the structure of a network. In an homogeneous network the number of inputs directed to each cell is constant and it is called the network valency. In this talk, we focus on bifurcations in coupled cell systems with a condition associated to the network valency. Moreover, we address the lifting bifurcation problem that concerns whether all bifurcation branches are lifted from a small network to a bigger one. We present some results and examples about this problem.