A model for the convective; flow in a fluid-saturated porous medium containing a reactive component is considered. This component undergoes an exothermic reaction (modelled by a first order mechanism) on an impermeable bounding surface, the resulting heat released driving the convective Bow Large Rayleigh number Bow near a stagnation point is treated in detail by first considering the steady states. Multiple solution branches and critical points arising from a hysteresis bifurcation are identified. The form that these solution branches take depends on whether or not the effects of reactant consumption are included. An initial-value problem is then discussed. This shows that both the lower (slow reaction) and upper (fast reaction) solution branches are stable (and the ultimate state of the system). When the parameter values are such that there is no steady state, the solution develops a finite-time singularity, the nature of which is analysed.