We study in details the deformations of a liquid-liquid interface induced by the electromagnetic radiation pressure of a focused cw laser beam. Using a simple linear model of static equilibrium of the interface under the effect of radiation pressure, buoyancy and Laplace pressure, we explain the observed hump height variations for any value of the optical Bond number Bo = (omega 0/lc)² (lc is the capillary length and !0 is the waist of the beam) in the regime of weak deformations, and show that the deformations are independent of the direction of propagation of the laser. Increasing the beam power, we observe an instability of the interface leading to the formation of a long jet when the laser propagates from the more refringent phase to the less refringent one. We propose that the total internal reflection of the incident light on the highly deformed interface could be at the origin of this instability. Using a nonlinear model of static equilibrium of the interface taking account of the angular dependance of radiation pressure, we explain the observed beam power threshold of the instability as well as the shape of the interface deformations observed at large waists just below the instability onset. According to this model, the instability should occur when the interface slope reaches the angle of total reflection teta TR. We find that the maximum incidence angle along the interface teta i max just below the instability threshold is significantly smaller than teta TR, and that our nonlinear model does not present any instability up to teta i max = teta TR, making the proposed instability mechanism qualitatively rough although quantitatively accurate. We finally discuss possible additional effects that could explain the instability.< Réduire