Effects of positive flame stretch on laminar burning velocities, and conditions for transition to unstable flames, were studied experimentally for freely propagating spherical flames at both stable and unstable preferential-diffusion conditions. The data base involved new measurements for H-2/O2/N2 mixtures at values of flame stretch up to 7600 s-1, and existing measurements for C3H8/O2/N2 mixtures at values of flame stretch up to 900 s-1. Laminar burning velocities varied linearly with increasing Karlovitz numbers-either decreasing or increasing at stable or unstable preferential-diffusion conditions-yielding Markstein numbers that primarily varied with the fuel-equivalence ratio. Neutral preferential-diffusion conditions, however, were shifted toward the unstable side of the maximum laminar burning velocity condition that the simplest preferential-diffusion theories associate with neutral stability. All flames exhibited transition to unstable flames: unstable preferential-diffusion conditions yielded early transition to irregular flame surfaces, and stable preferential-diffusion conditions yielded delayed transition to cellular flames by hydrodynamic instability. Conditions for hydrodynamic instability transitions for H2/O2/N2 mixtures were consistent with an earlier correlation due to Groff for propane/air flames, based on the predictions of Istratov and Librovich.