Phase separation experiments have been performed on mixtures of colloidal polyisobutene grafted boehmite rods and flexible polymers. Two systems of rods have been studied, one with an average length and diameter of 71 nm and 11.1 nm, and the other with an average length and diameter of 253 nm and 9.4 nm. The polymers used have molecular weights varying from 35 to 186 kg mol(-1), leading to radii of gyration of 5.9 to 20 nm. Bi- and triphasic equilibria involving a dilute isotropic phase, a concentrated isotropic phase, and a nematic phase are observed, The phase behavior is compared to a recent theory, which is an extension of the treatment for sphere/polymer mixtures (H. N. W. Lekkerkerker ef al., Europhys. Left, 20, 559 (1992)). The main features of the phase behavior can be understood on the basis of this simple theory. There remain significant discrepancies between theory and experiment which are attributed to the limitations of the theory on the one hand and to the polydispersity of the colloidal rods and the formation of metastable and nonequilibrium states such as colloidal gels and glasses on the other hand.