The dynamics of fuel-lean (equivalence ratio phi = 0.5) premixed hydrogen/air flames are investigated numerically in a 2-mm-height planar channel with platinum-coated walls, as a function of the inlet velocity and catalytic reactivity. An elliptic 2-D transient code is used, with elementary heterogeneous (catalytic) and homogeneous (gas-phase) chemical reaction schemes and detailed transport. The channel wall temperature is prescribed and the inlet properties are uniform. The catalytic reactivity is controlled by varying the model parameter A(s), which denotes the ratio of the catalytically active area to the geometrical channel surface area. It is shown that the rich flame dynamics of the non-catalytic case (A(s) = 0), which include non-stationary repetitive ignition/extinction and oscillating flames, can be suppressed by suitable selection of the catalytic reactivity. The repetitive/ignition extinction flames are eliminated at A(s) = 0.003 and the oscillating ones for A(s) > 0.01, while for higher values of A(s) only stationary "closed symmetric" and "asymmetric" flames are obtained. The results suggest that the application of a predetermined catalyst loading on the channel walls is a feasible method to eliminate unsteady combustion modes in practical mesoscale reactors. (C) 2010 Elsevier B.V. All rights reserved.