ABSTRACT We have carried out 2D hydrodynamical simulations to study the effects of disc self-gravity and radiative cooling on the formation of gaps and spirals. (1) With disc self-gravity included, we find stronger, more tightly wound spirals and deeper gaps in more massive discs. The deeper gaps are due to the larger Angular Momentum Flux (AMF) of the waves excited in more massive discs, as expected from the linear theory. The position of the secondary gap does not change, provided that the disc is not extremely massive (Q ≳ 2). (2) With radiative cooling included, the excited spirals become monotonically more open (less tightly wound) as the disc’s cooling time-scale increases. On the other hand, the amplitude and strength of the spirals decrease when the cooling time increases from a small value to ∼1/Ω, but then the amplitude starts to increase again when the cooling time continues to increase. This indicates that radiative dissipation becomes important for waves with Tcool ∼ 1. Consequently, the induced primary gap is narrower and the secondary gap becomes significantly shallower when the cooling time becomes ∼1/Ω. When the secondary gap is present, the position of it moves to the inner disc from the fast cooling cases to the slow cooling cases. The dependence of gap properties on the cooling time-scale (e.g. in AS 209) provides a new way to constrain the disc optical depth and thus disc surface density.