The effects of heat capacity lag on the flow over slender bodies are examined via an extension of Ward's (1949) generalised treatment of the slender body problem. The results are valid for smooth bodies of arbitrary cross-sectional shape and attitude in the complete Mach number range up to, but not including, hypersonic. Transonic flow can be treated owing to the presence of a dissipative mechanism in the basic differential equation, but the results in this Mach number range are probably of limited practical value. The results show that cross-wind forces are unaffected in a first approximation, but that drag forces comparable with laminar skin friction values can arise as a result of the relaxation of the internal degrees of freedom. The magnitude and sign of these effects depend strongly on body shape and free stream Mach number. Results are given for surface pressure coefficient and the variations of translational and internal mode temperature on and near the body are also found. The influence of these latter effects on heat transfer to the body is discussed.