Summary: The propagation of planar reaction-diffusion waves in the isothermal autocatalytic system \(A + mB \to (m+1)B\), rate \(kab^ m\), is considered. Attention is paid to the case when the diffusion coefficient of reactant \(A\) is much less than that of the autocatalyst; the case when \(A\) is completely immobilized is discussed in detail. Permanent-form travelling waves are initiated and their structure is treated. It is found that for sufficiently large values of \(m\) this steady wave structure becomes unstable to longitudinal disturbances and an oscillatory wave structure develops. The structure of this propagating oscillatory reaction- diffusion front is also discussed.