We present accretion rates for a large number of solar-type stars in the Cep OB2 region, based on U-band observations. Our study comprises 95 members of the ~4Myr old cluster Tr 37 (including 20 "transition" objects (TOs)), as well as the only classical T Tauri star (CTTS) in the ~12Myr old cluster NGC 7160. The stars show different disk morphologies, with the majority of them having evolved and flattened disks. The typical accretion rates are about 1 order of magnitude lower than in regions aged 1-2Myr, and we find no strong correlation between disk morphology and accretion rates. Although half of the TOs are not accreting, the median accretion rates of normal CTTS and accreting "transition" disks are similar (~3x10^-9^ and 2x10^-9^M_{sun}_/yr, respectively). Comparison with other regions suggests that the TOs observed at different ages do not necessarily represent the same type of objects, which is consistent with the fact that the different processes that can lead to reduced IR excess/inner disk clearing (e.g., binarity, dust coagulation/settling, photoevaporation, giant planet formation) do not operate on the same timescales.