The effect of nonaxisymmetry on Alfven modes in toroidal geometry is investigated numerically. A model equation is used which simplifies the analysis on the resonant surfaces. Alfven modes, characterized by their poloidal and toroidal node numbers (m,n), are found to exist in moderate nonaxisymmetry as well. For fixed (m,n), however, the mode collapses from a global feature on the resonant surface into an infinitely thin Alfven ballooning mode along a field line, if the nonaxisymmetry exceeds a critical threshold or, with given nonaxisymmetry, if the poloidal variation does so. Alfven balloonings are polarized within the magnetic surfaces and are stable.