We report the observation of highly nonlinear vibrational relaxation for a number of large molecules in shock waves, together with an attempt at a master-equation modeling of this phenomenon. In all these molecules laser-schlieren measurements show a clear and often well-resolved local maximum in the density gradient, indicating a similar maximum in the rate of energy transfer. This unexpected phenomenon is seen in the relaxation of benzene (C6H6), cubane (C8H8), cyclopropane (C3H6), furan (C4H4O), norbornadiene (C7H8), oxirane (C2H4O), and quadricyclane (C7H8). It has also been detected in cyclopentadiene (C5H6) and pyrazine (C4N2H4), as well as CF3Br and CF3Cl but in these was not well resolved. The phenomenon thus seems nearly ubiquitous; of the "large" molecules where relaxation could be resolved, only norbornene (at C7H10 the largest such molecule) exhibits a fully linear relaxation. The gradients are clearly and solely from vibrational relaxation; integrated gradients are in good agreement with thermodynamic calculations of total density change, and near-equilibrium relaxation times in pure cyclopropane and oxirane are fully consistent with overlapping ultrasonic results. It appears we are seeing a delay in the development of series coupling in these experiments. An attempt is made to model the process using a linear master equation with exponential gap probabilities having an alpha(similar to (down)) linear in energy. Although this does introduce sufficient nonlinearity through the rate coefficients to produce maxima, these and the overall gradients are consistently too small. It is suggested that inclusion of a true nonlinearity through VV transfer will be needed to explain the observations, and a possible mechanism for this is proposed.