Using the disc instability model and a simple but physically reasonable model for the X-ray, extreme UV, UV and optical emission of dwarf novae we investigate the time lags observed between the rise to outburst at different wavelengths. We find that for ``normal'', i.e. fast-rise outbursts, there is good agreement between the model and observations provided that the disc is truncated at a few white dwarf radii in quiescence, and that the viscosity parameter alpha is ~ 0.02 in quiescence and ~ 0.1 in outburst. In particular, the increased X-ray flux between the optical and EUV rise and at the end of an outburst, is a natural outcome of the model. We cannot explain, however, the EUV delay observed in anomalous outbursts because the disc instability model in its standard alpha -prescription form is unable to produce such outbursts. We also find that the UV delay is, contrary to common belief, slightly longer for inside-out than for outside-in outbursts, and that it is not a good indicator of the outburst type.