Context. The disc instability model (DIM) has been very successful in explaining the dwarf nova outbursts observed in cataclysmic variables. When, as in intermediate polars, the accreting white dwarf is magnetised, the disc is truncated at the magnetospheric radius, but for mass-transfer rates corresponding to the thermal-viscous instability such systems should still exhibit dwarf-nova outbursts. Yet, the majority of intermediate polars, in which the magnetic field is not large enough to completely disrupt the accretion disc, seem to be stable, and the rare observed outbursts, in particular in systems with long orbital periods, are much shorter than normal dwarf-nova outbursts.Aims. We investigate the predictions of the disc instability model for intermediate polars in order to determine which of the observed properties of these systems can be explained by the DIM.Methods. We use our numerical code for the time evolution of accretion discs, modified to include the effects of the magnetic field, with constant or variable mass transfer from the secondary star.Results. We show that intermediate polars have mass transfer low enough and magnetic fields large enough to keep the accretion disc stable on the cold equilibrium branch. We show that the infrequent and short outbursts observed in long-period systems, such as, for example, TV Col, cannot be attributed to the thermal-viscous instability of the accretion disc, but instead have to be triggered by an enhanced mass-transfer from the secondary, or, more likely, by some instability coupling the white dwarf magnetic field with that generated by the magnetorotational instability operating in the accretion disc. Longer outbursts (a few days) could result from the disc instability.Key words: accretion, accretion disks / stars: dwarf novae / instabilities