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We investigate some aspects of the general problem of nonlinear effects on the operation of an anisotropic ladder of Josephson junctions with injected ac currents. We predict the existence of attracting time-periodic spatially localised modes, for some ranges of junction characteristic parameters. These elementary dynamical excitations are of two different types, associated to oscillatory and rotating motion of a few superconducting islands phases, respectively, revealing a dynamical mechanism of creation of vortex-antivortex pairs. These results are physical applications of recent advances in the theory of nonlinear dynamics of discrete macroscopic systems. Their experimental confirmation would probe the physical relevance of localisation in Josephson-junction devices.