Current-vortex filament solutions to the two-fluid plasma equations that describe drift-Alfvén waves are presented. Such filament systems are Hamiltonian. Integrable three and four filament systems are discussed in some detail. A wide variety of orbit topologies exists in the plasma case. Special attention is paid to collapses where all filaments contract to a single point. The differences and extensions with respect to point vortex solutions in two-dimensional (2D) incompressible Euler systems is pointed out.