In this work, we revisit the topic of surface waves on nonreciprocal plasmonic structures, and clarify whether strictly unidirectional surface plasmon-polaritons are allowed to exist in this material platform. By investigating different three-dimensional configurations and frequency regimes, we theoretically show that, while conventional surface magneto-plasmons are not strictly unidirectional due to nonlocal effects, consistent with recent predictions made in the literature, another important class of one-way surface plasmon-polaritons, existing at an interface with an opaque isotropic material, robustly preserve their unidirectionality even in the presence of nonlocality, and for arbitrarily-small levels of dissipation. We also investigate the extreme behavior of terminated unidirectional waveguiding structures, for both classes of surface waves, and discuss their counter-intuitive implications.