Abstract : We study two separate models for yeast cell-cell communication. Each model consists of a coupled system of two non-linear, non-local equations in one dimension of space. The first model describes the two cells in the transversal direction, orthogonal to the membrane, whereas the second model describes the two cells in the tangential direction, along the membrane. We study long time dynamics for each model, ranging from convergence to stable steady states (bistability in model 1), to possible finite time blow-up (formation of singularity in model 2). The biological interpretation of the mathematical results is discussed.