Higher order terms in the outer asymptotic expansions for flows of slender streams in the presence of gravity are computed. In particular, for the case of jet flow, higher order terms corresponding to a basic flow with either a circular or elliptical cross‐sectional shape are discussed in detail and an inherent spatial instability (due to the effects of gravity) in the jet is discussed. Higher order terms for pipe flow and channel flow are also calculated and an example is presented. The pressure distribution within the flow is also computed and the effects of the pressure on the flow when a free surface is present is discussed.