In this thesis the possibility of nonlinear ultrasonic NDT is investigated for complex materials and biological tissues. The delayed TR-NEWS signal processing methodis developed, which is based on the TR-NEWS method. TR-NEWS is a method well-suited for materials with complex structure: it allows spatio-temporal focusing of a long ultrasonic chirp signal to the region near the receiving transducer, forming an impulse pulse. The received signal power and SNR are increased as a result.Delayed TR-NEWS allows the use of this focused wave pulse as a new basis for either the signal optimisation or, alternatively, for the detection of nonlinearity by the breakdown of linear superposition. This method is used in physical experiments and simulations. The physical experiments are made on an undamaged CFRP block and a porcine skin sample. The skin is tested in a synchronised acoustomechanical setup specially designed in the course of this thesis. In 1D pseudospectral simulations for CFRP, it is determined that while classical nonlinearity cannot probably be detected in ultrasonic NDT, it could be possible to detect nonclassical nonlinear effects such as those from cracks and microdamage.Physical experiments and 2D FEM simulations of linear, undamaged CFRP are compared for studying the delayed TR-NEWS method, its applicability in optimising the focused wave, and also for creating an interaction of waves at the focusing region with a linear superposition prediction. This suggests the possibility of detecting nonlinearities by comparing the actual signal from interaction to the linear prediction.Finally, more 2D simulations are conducted for CFRP with a single contact gap nonlinearity near the focusing region. The nonlinearity is measured by PI and delayed TR-NEWS. It is determined that delayed TR-NEWS is able to detect the defect at least as well as the PI method. It is ascertained that the PM hysteresis model could describe the nonclassical nonlinearity of damaged materials and biological tissues. Asynchronised acoustomechanical test setup is created to test such multiscale nonlinearity. The simultaneous mechanical load test and ultrasonic delayed TR-NEWS test can be used to measure the mechanical properties of skinNous proposons l’innovation «TR-NEWS retardée» comme une extension des méthodes TR-NEWS,issues de la symbiose du retournement temporel (RT) et des méthodes de spectroscopie d’ondes élastiques non linéaires (NEWS), avec pour principales applications le contrôle non destructif (CND) et l’imagerie ultrasonore médicale. Nous confirmons expérimentalement les bonnes performances des méthodes TR-NEWS pour : (i) des échantillons de composite CFRP aux propriétés dispersives ultrasonores autour de 10 MHz, favorisant ainsi la réverbérabilité de la propagation acoustique; (ii) des mesures de propriétés non classiques de la peau porcine par une instrumentation multi-échelles acousto-mécanique élaborée dans le cadre du projet PLET(Propriétés Locales Visco-Élastiques de la peau par TR-NEWS) financé par la Région Centre Val de Loire. via les simulations numériques 1D pseudo spectrales de propagations acoustiques non linéaires dans les CFRP, nous identifions et localisons les sources locales de défauts et de microendommagements. Elles valident l’identification d’un crack unique proche de la zone de focalisation. La non linéarité supposée de type contact acoustique (CAN),mesurée par «TR-NEWS retardée»et comparée aux techniques classiques d’inversion d’impulsion utilisées en imagerie médicale, permet une identification préservant la représentation temporelle de l’information. Ainsi, ce système d’instrumentation acousto-mécanique envisage la mesure de paramètres multi-échelles de non linéarité des tissus biologiques via les paramètres de Preisach-Mayergoyz (espaces PM) permettant de décrire leur vieillissement. Le chargement basse fréquence uniaxial (0.1-10Hz) synchronisé aux caractérisations ultrasonores haute fréquence (20MHz) via «TR-NEWS retardé» suggère une nouvelle classe de dispositifs dotée d’une perspective de multimodalité dédiée à l’imagerie ultrasonore non invasive des propriétés biomécaniques des organismes vivants