||We present an exhaustive analysis of transport measurements performed in twinned YBa2Cu3O7 single crystals which establishes that the vortex solid-liquid transition is first order when the magnetic field H is applied at an angle ? away from the direction of the twin planes. We show that the resistive transitions are hysteretic and the V-I curves are nonlinear, displaying a characteristic S shape at the melting line Hm(T), which scales as ?(?)Hm(T,?), where ?(?) is the anisotropy factor. These features are gradually lost when the critical point H*(?) is approached. Above H*(?) the V-I characteristics show a linear response in the experimentally accessible V-I window, and the transition becomes reversible. Finally we show that the first-order phase transition takes place between a highly correlated vortex liquid in the field direction and a solid state of unknown symmetry. As a consequence, our data support the scenario for a vortex-line melting in twinned YBa2Cu3O7 crystals in contrast to a vortex sublimation as recently suggested for untwinned La2-xSrxCuO4, YBa2Cu3O7 and Bi2Sr2CaCu2O8 [T. Sasagawa et al., Phys. Rev. Lett. 80, 4297 (1998)].