We study the kinematics of gaseous discs in triaxial dark matter haloes using the closed-loop orbit solutions in non-axisymmetric potentials. The orbits are in general non-circular and, for a given triaxiality, their ellipticity depends on the ratio of escape to circular velocities, V2esc/V2c. This ratio increases steeply towards the centre for cold dark matter (CDM) halo density profiles, implying that even minor deviations from spherical symmetry may induce large deviations from circular orbits in the velocity field of a gaseous disc, especially near the centre. This result suggests that caution should be exercised when interpreting constraints on the presence of density cusps in the dark halo derived from the innermost velocity profile. Simulated long-slit rotation curves vary greatly in shape, depending primarily on the viewing angle of the disc and on its orientation relative to the principal axes of the potential. ‘Solid-body’ rotation curves – typically interpreted as a signature of a constant density core in the dark matter distribution – are often obtained when the slit samples velocities near the major axis of the closed-loop orbits. Triaxial potentials imprint specific symmetries in 2D velocity fields, generally inducing ‘twists’ in the isovelocity contours and antisymmetric patterns in opposite quadrants. We suggest that triaxial haloes may be responsible for the variety of shapes of long-slit rotation curves of low surface brightness (LSB) galaxies, as well as for the complex central kinematics of LSBs, which are sometimes ascribed to the presence of ‘radial motions’ in the gas. We argue that LSB rotation curves might be reconciled with the structure of CDM haloes once the effects of halo triaxiality on the dynamics of gaseous discs are properly taken into account.