Local transport in the L (low βp) and H (high βp) types of double-null divertor discharges in ASDEX is investigated by computer modelling. For the L type, two subregimes with different local transport behaviour can be distinguished: Homogeneous electron heat diffusivities χe = e or flat χe profiles and diffusion coefficients D = 0.2 χe are found for e < 5.2 x 104 cm2·s–1 (L-I), while above this limit, steep χe and flat D profiles are determined (L-II). The observed decrease in energy confinement time with increasing neutral injection power is found to be due to enhancement of the electron heat diffusivity. In the L-II regime, χe strongly increases with radius, while the diffusion coefficient remains flat. The diffusivities show a rather weak dependence on time as in the L-I regime. In both L regimes they rise with increasing injection power and decreasing plasma current, but are independent of density. In the H regime, transport is characterized by flat χe profiles and D = 0.2 χe. The diffusivities are reduced by a factor of about two in the whole plasma compared with the L type. They show the variation with plasma current found in L discharges and are also independent of density. One more common feature of L and H regimes is that the ion heat diffusivity is in the range of 1 to 3 times the neoclassical values.