Stretched laminar flame velocities in stoichiometric finite thickness H-2/air and CH4/air flames at atmospheric pressures-investigated through an implicit direct simulation method are that features the coupling of the fully compressible flow to the realistic chemistry and multicomponent transport properties. The method resolves all the chemical and flow length and time scales, which is essential for investigating highly stiff reacting flow systems with realistic chemistry. Eight flame configurations are investigated: outwardly and inwardly propagating H2/air and CH4/air in cylindrical and spherical geometries. Nonlinear power law relationships are observed between the velocity deficit S-L - S-n and the flame curvature 1/r(u), viz S-L - S-n similar to (1/r(u))(p) with 0 < p < 1, where p depends upon the flame type and the propagation mode. (S-L is the unstretched laminar flame velocity, and S-n is the stretch flame velocity, r(u) is the flame radius of curvature.) The Markstein linear hypothesis for asymptotically thin flames corresponds to p = 1; our results show that such a linear hypothesis cannot be extended to realistic finite thickness flames under the conditions of the study. The outwardly propagating H-2/air flames are an exception, displaying an entirely different anomalous non-power law relationship, which is indicative of the complex coupling between the thermochemistry and flame geometry.