Two-transverse-mode vertical cavity surface emitting lasers (VCSELs) subject to external optical injection is experimentally investigated. The spectra of the VCSEL with two parallel-polarized modes, under optical injection, demonstrate significantly different behaviors, compared to the VCSEL with two orthogonally-polarized transverse modes. In a VCSEL with two orthogonally-polarized transverse modes, the experimental results are good qualitative agreement with the theoretical prediction that the external optical injection can be used to achieve single-mode operation. However, in the case of a two parallel-polarized transverse modes VCSEL, single-mode operation cannot be obtained via optical injection. When the injection frequency is close to one of the modes, the coexistence of the injected beam and the mode gives rise to very rich dynamical behavior, however, the other mode is unperturbed by the optical injection.