A model for a differential-flow reactor is considered, based on cubic autocatalator kinetics in which the substrate is immobilized and the autocatalyst flows through the reactor at a constant rate. Linear stability analysis shows that there is a critical flow rate above which the spatially uniform steady state becomes convectively unstable, Numerical simulations show that this convective instability leads to the formation of a wave packet propagating through the reactor. The nature of this wave packet depends on the flow rate and on the two cases that are identified for the kinetic parameter mu, namely a generic case for general values of mu and when mu is close to the value which gives a Hopf bifurcation in the kinetic system.