Audio rendering systems are always slightly nonlinear. Their non-linearities must be modeled and mea- sured for quality evaluation and control purposes. Cascade of Hammerstein models describes a large class of non-linearities. To identify the elements of such a model, a method based on a phase property of exponential sine sweeps is proposed. A complete model of non-linearities is identified from a single mea- surement. Cascade of Hammerstein models corresponding to an electro-dynamic loudspeaker are identified this way. Harmonic distortion is afterward predicted using the identified models. Comparisons with clas- sical measurements techniques show that harmonic distortion is accurately predicted by the identified models over the entire audio frequency range for any desired input amplitude.