The spectrum of baroclinic basin modes is investigated in a two-layer wind-driven quasigeostrophic model through weakly-nonlinear multiple-time-scale expansion in the Burger number. The baroclinic basin modes are mainly advected by a barotropic steady Sverdrup flow. Emphasis is given to the regularizing influence of dispersion rather than to dissipation. In the inviscid large-scale limit, i.e. for basin scale considerably larger than the Rossby radius of deformation, all the basin modes are neutral. Their typology is then numerically examined (with some necessary dissipation), and their frequency and spatial properties are discussed. Three types of modes arise for some wind forcing strong enough to produce a recirculating gyre with closed geostrophic contours: the classical Rossby basin modes deformed by the mean flow (shadow modes), stationary modes and recirculating pool modes, the two latter being trapped in the closed-contours pool. Focus is made, here, on the recirculating modes that could have very low frequencies for moderate recirculating gyres. Strong gyres lead to higher frequencies, and recirculating modes resonate with deformed Rossby basin modes.