This paper deals with the characterisation and modelling of the nonlinear viscoelasticity properties of concentrated oil-in-water emulsions containing sunflower oil (60-80 wt%), water and a hydrophilic sucrose palmitate (1-5 w%). With this aim, transient shear flow and nonlinear stress relaxation tests were carried out. Oscillatory shear measurements were also performed to calculate the linear relaxation modulus of the emulsions studied. The transient how behaviour of all the emulsions studied is qualitatively similar, showing always a stress overshoot followed by a stress decay which tends to a steady-state value. However, at a critical shear rate, which depends on temperature and disperse phase concentration, a stress undershoot may be found. This behaviour has been attributed to optically observed shear-induced microstructural changes. A factorable nonlinear viscoelastic constitutive equation, the Wagner model with Soskey-Winter＇s damping function, predicts the transient flow of these emulsions, in a range of shear rates, fairly well. However, a lack of concordance is found as shear rate increases, fact that has been explained on the basis of wall-slip phenomena and shear-induced microstructural changes.