Low-lying multiphonon states in 136 Ba have been populated with the inelastic neutron scattering reaction. Excitation functions were performed at neutron energies from 2.2 to 3.9 MeV, and γ -ray angular distributions were measured at 2.5, 3.0, and 3.5 MeV. Lifetimes have been determined using the Doppler-shift attenuation method, and electromagnetic transition rates have been deduced. The previously assigned 2 + 1,ms mixed-symmetry state at 2128.9 keV has been confirmed and is not greatly fragmented. For the first time in the N = 80 isotones, a 3 + 2,ms two-phonon mixed-symmetry state is proposed. In addition, the 2 + 5 and the 4 + 3 levels at 2222.7 and 2356.4 keV, respectively, decay with large B(M1) values to the two-phonon 2 + 2 and 4 + 1 states, respectively, which suggests two-phonon mixed-symmetric character. Their excitation energies, however, are not consistent with this interpretation.