In this paper certain steady equivalent-barotropic oceanic boundary currents are presented. They all have the property of being resistant to small-amplitude quasi-geostrophic perturbations of any spatial form. Such a stability property has been determined by making use of a method originally proposed by Arnold and whose importance for flows over a flat bottom was recently called in question by Andrews in the atmospheric context. The very existence of these simple oceanic currents, whose stability can be checked via the above-mentioned method, suggests that Arnold's stability criterion can be in principle a powerful tool for analysing the stability of more realistic oceanic flows, even in the absence of topographic forcing.