Previous molecular dynamics simulations of friction between polymer brushes in relative sliding motion [Kreer, T.; Muser, M. H.; Binder, K.; Klein, J. Langmuir 2001, 17, 7804] are extended beyond steady-state conditions. We study two different protocols: (i) stop and return and (ii) stop and go. In protocol (i), the relative, lateral motion between the two surfaces is stopped abruptly and reimposed opposite to the initial direction after the system could relax for some time. Protocol (ii) is similar except that the sliding direction is maintained. In the constant-velocity steady state, the average lateral extension l(c) of the polymers is found to be a power law of the sliding velocity upsilon, namely, l(c) proportional to upsilon(0.3). When the sliding direction is inverted, a shear stress maximum is observed after the two walls have slid a relative distance of 2l(c). This maximum occurs when the average inclination of the polymers is 90degrees, and it is accompanied by brush swelling. In protocol (ii), no brush swelling is found and shear stress maxima are absent in the itinerant stages of the go phase, with the exception of large upsilon. We conclude that dissipation mechanisms for oscillatory shear are similar to those for constant-velocity sliding if the driving amplitude A distinctly exceeds 2l(c). Moreover, enhanced loss at l approximate to 2l(c) is not necessarily related to stick-slip motion.