The paper is concerned with the study of an integro-differential equation of the type: \[ u_ t=\int^{t}_{-\infty}K(t,s) u_{xx}(x,s) ds+Ru- u^ 3 \] with boundary conditions \(u=0\) for \(x=0\), where the kernel K is of Maxwell or Jeffrey type depending thus on one or more parameters, and R is a parameter that corresponds to the Rayleigh number. The problem is modelling the presence of memory in viscoelastic fluids. The problem is transformed into a pair of coupled differential equations for which the linearized stability is studied. For the nonlinear problem the extent of the memory is shown to give the steady or the periodic bifurcation as R is increased. Approximate solutions are obtained by using Fourier series that enable, by truncation, to reduce the problem to ordinary differential equations.