An oblique detonation wave in two-phase kerosene–air mixtures over a wedge is numerically studied for the first time. The features of initiation and stabilisation of the two-phase oblique detonation are emphasised, and they are different from those in previous studies on single-phase gaseous detonation. The gas–droplet reacting flow system is solved by means of a hybrid Eulerian–Lagrangian method. The two-way coupling for the interphase interactions is carefully considered using a particle-in-cell model. For discretisation of the governing equations of the gas phase, a WENO-CU6 scheme (Hu et al., J. Comput. Phys., vol. 229 (23), 2010, pp. 8952–8965) and a sixth-order compact scheme are employed for the convective terms and the diffusive terms, respectively. The inflow parameters are chosen properly from real flight conditions. The fuel vapour, droplets and their mixture are taken as the fuel in homogeneous streams with a stoichiometric ratio, respectively. The effects of evaporating droplets and initial droplet size on the initiation, transition from oblique shock to detonation and stabilisation are elucidated. The two-phase oblique detonation wave is stabilised from the oblique shock wave induced by the wedge. As the mass flow rate of droplets increases, a shift from a smooth transition with a curved shock to an abrupt one with a multi-wave point is found, and the initiation length of the oblique detonation increases, which is associated with the increase of the transition pressure. By increasing the initial droplet size, a smooth transition pattern is observed, even if the equivalence ratio remains constant, and the transition pressure decreases. The factor responsible is incomplete evaporation before the detonation fronts, which results in a complicated flame structure, including regimes of formation of oblique detonation, evaporative cooling of droplets and post-detonation reaction.