A dynamical effect of coherent backscattering is predicted theoretically and supported by computer simulations: The distribution of single-mode delay times of waves reflected by a disordered waveguide depends on whether the incident and detected modes are the same or not. The change amounts to a rescaling of the distribution by a factor close to sqrt(2). This effect appears only if the length of the waveguide exceeds the localization length; there is no effect of coherent backscattering on the delay times in the diffusive regime.