A continuous-discontinuous model to simulate numerically an entire failure process is presented. Crack inception and its propagation is modelled by means of a gradient non-local model based on non-local displacements. To simulate properly the final stages of the process, a discrete crack approach (X-FEM) is used, where both local and non-local displacements are modelled as discontinuous fields. In this paper, this new combined approach is studied in detail and one- and two-dimensional examples are carried out to validate it.