AbstractWe present numerical experiments that demonstrate that the nonlinear development of the Toomre instability in disks of isothermal gas, stars, and dark matter reproduces the observed Schmidt Law for star formation. The rate of gas collapse depends exponentially on the (minimum) value of the Toomre parameter in the disk. We demonstrate that spurious fragmentation occurs in the absence of sufficient resolution in our SPH model. Our models also reproduce observed star formation thresholds in disk galaxies. We finally briefly discuss the application of our models to the study of globular cluster formation in merging galaxies.