Two-colour polarization labelling experiments have been used to explore the excitation spectrum of the rubidium dimer in the region 25 500–27 000 cm−1, probing two mutually interacting states, identified from ab initio calculations as the 51Σ+u and 51Πu states whose atomic dissociation products are Rb(5s) + Rb(5d). Treating the rather irregular progressions observed in the excitation spectra as transitions to single states with (numerous) local perturbations, we propose spectroscopic parameters and potential energy curves to describe the investigated levels. Observations cover more than 20 vibrational levels in the inner minima of both the 51Πu and 51Σ+u states. Analysis was guided by ab initio calculations performed to describe the 1,3Λg,u electronic states of Rb2 up to the Rb(5s) + Rb(5f) atomic asymptote. The theoretical potential energy curves are given in ASCII format in an electronic supplement to this paper.