The paper is devoted to modelling of cell dierentiation in an initially homogeneous cell population. The mechanism which provides coexistence of two cell lineages in the initially homogeneous cell population is suggested. If cell dierentiation is initiated locally in space in the population of undierentiated cells, it can propagate as a travelling wave converting undierentiated cells into dierentiated ones. We suggest a model of this process which takes into account intracellular regulation, extracellular regulation and dierent cell types. They include undierentiated cells and two types of dierentiated cells. When a cell dierentiates, its choice between two types of dierentiated cells is determined by the concentrations of intracellular proteins. Dierentiated cells can either stimulate dierentiation into their own cell lineage or into another cell lineage. In the case of the positive feedback, only one lineage of dierentiated cells will nally appear. In the case of negative feedback, both of them can coexist. In this case a periodic spatial pattern emerges behind the wave.