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Context. Although the disc instability model is widely accepted as the explanation for dwarf nova outbursts, it is still necessary to confront its predictions to observations because much of the constraints on angular momentum transport in accretion discs are derived from the application of this model to real systems. Aims. We test the predictions of the model concerning the multicolour time evolution of outbursts for two well--observed systems, SS Cyg and VW Hyi. Methods. We calculate the multicolour evolution of dwarf nova outbursts using the disc instability model and taking into account the contribution from the irradiated secondary, the white dwarf and the hot spot. Results. Observations definitely show the existence of a hysteresis in the optical colour-magnitude diagram during the evolution of dwarf nova outbursts. We find that the disc instability model naturally explains the existence and the orientation of this hysteresis. For the specific cases of SS Cyg and VW Hyi, the colour and magnitude ranges covered during the evolution of the system are in reasonable agreement with observations. However, the observed colours are bluer than observed near the peak of the outbursts -- as in steady systems, and the amplitude of the hysteresis cycle is smaller than observed. The predicted colours significantly depend on the assumptions made for calculating the disc spectrum during rise, and on the magnitude of the secondary irradiation for the decaying part of the outburst. Conclusions. Improvements of the spectral disc models are strongly needed if one wishes to address the system evolution in the UV.