Polymer degradation occurs when macromolecular chains are broken under the influence of thermal, mechanical or chemical energy. Chain-end depolymerization and random- and midpoint-chain scission are mechanisms that have been observed in liquid-phase polymer degradation. Here we develop mathematical models, unified by continous-mixture kinetics, to show how these different mechanisms affect polymer degradation in solution. Rare expressions for the fragmentation of molecular-weight distributions (MWDs) govern the evolution of MWDs. The governing integrodifferential equations can be solved analytically for realistic conditions. Moment analysis for first-order continuous kinetics shows the temporal behavior of MWDs. Chain-end depolymerization yields monomer product and polymer molecular-weight moments that vary linearly with time. In contrast, random- and midpoint-chain scission models display exponential time behavior The mathematical results reasonably describe experimental observations for polymer degradation. This approach, based on the time evolution of continuous distributions of chain length or molecular weight, provides a framework for interpreting several types of macromolecular degradation processes, particularly how bimodal MWDs can evolve during degradation.