Solutions of the Alfve´n wave continuum equation for a pressureless, magnetohydrodynamic plasma in nonaxisymmetric, toroidal geometry are presented. The analysis is based on the Hamiltonian form of the continuum equation along lines of force of the equilibrium magnetic field. Canonical transformation methods are invoked to determine approximate solutions of the continuum equation. The approximate solutions are used to identify the conditions that govern the Alfve´n continuous spectrum in nonaxisymmetric toroidal geometry.