A new method for the study of time reversal violation is described. It consists of measurements of the forward-backward asymmetry in individual gamma-ray transitions resulting from unpolarized neutron capture in p-wave resonances. An experiment with a 1,3 Cd target performed at the Dubna pulsed neutron source has been analyzed and a limit on the time reversal odd, parity even interaction extracted. The possibility of experiments using the powerful pulsed neutron source at Los Alamos is considered.PACS numbers: 25.40.Ny, 1 UO.Er CP nonconservation or T (time reversal) noninvariance was observed in the decay of neutral kaons long ago [1]. Attempts to search for this phenomenon in other processes have failed. Recently some possible tests using neutron optics experiments were discussed in a paper by Weidenmuller [2] and references therein. Interest in the neutron-nucleus interaction was stimulated by the discovery [3,4] of large P-(parity-) nonconserving effects near neutron p-wave resonances. These effects appeared to be enhanced by 3 to 6 orders of magnitude compared to the single-particle estimate Gm£ -10~7 (in units of h =c = 1 and G = \0~5m p~2 ).The enhancement was explained in terms of the P-nonconserving mixing of compound nuclear states with opposite parity (mixing of the p-wave resonance with the nearest s-wave resonances [5,6]). The concept of the spreading width of the weak interaction was brought into practice based on recent experimental results [7], It was shown by Bunakov and Gudkov [8,9] that possible T-noninvariant effects may be enhanced near p-wave resonances in the same manner as P-nonconserving effects. It has been suggested that a serach be made for P-conserving, T-noninvariant effects in polarized neutron transmission through aligned nuclear targets [10][11][12]. Such an effect would occur due to an s-[kxlKkl) term in the neutron-nucleus elastic forward scattering amplitude. Here s and I are the neutron and nucleus spins and k is neutron momentum. Bunakov [9] showed that the maximum value of the experimental polarization asymmetry in the cross section p is connected to the Tnoninvariant matrix element vj and to the /7-wave resonance level spacing D p by the approximate relation P^vJ/Dp.(1)