  We construct new classes of vortex-like solutions of the CP^N model in (3+1)
dimensions and discuss some of their properties. These solutions are obtained
by generalizing to (3+1) dimensions the techniques well established for the two
dimensional CP^N models. We show that as the total energy of these solutions is
infinite, they describe evolving vortices and anti-vortices with the energy
density of some configurations varying in time. We also make some further
observations about the dynamics of these vortices.
