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The behaviours of a pipe conveying fluid and a fluid loaded panel are studied from the viewpoint of differentiable dynamics. Non-linear terms are included and it is shown how the partial differential equation of motion can be recast, by Galerkin's method and modal truncation, in the form of an ordinary differential equation in Euclidean n-space. This evolution equation is then analysed qualitatively, attention being paid to bifurcations which occur as the control parameters of axial force and flow velocity are varied. Bifurcations of fixed points occur when at least one of the eigenvalues of the linearized evolution equation crosses the imaginary axis in the complex plane. In this situation, centre manifold theory can be used to extract a low dimensional subsystem which completely captures the local bifurcational behaviour. Such essential models enable the onset of divergence and flutter to be analysed relatively simply and …