In the present study we examine Rayleigh flows of single-phase, nonreacting fluids. When the fluid is of the Bethe-Zel'dovich-Thompson type, it is shown that as many as three sonic points and extrema of the entropy, enthalpy, and heat supply can occur on a fixed Rayleigh line. Exact solutions for van der Waals gases are provided, as is a complete theory of shocked and unshocked flows subjected to strict heating or strict cooling. Further nonclassical results of interest include the occurrence of flow choking in unshocked and shocked strictly cooled flows, the occurrence of as many as three shock waves in cooled or heated flows, and shock splitting in both cooled and heated flows.