Following a review of the processing of functionally graded metals and metal-ceramic composites in Part 1; this Part 2 of the two part series focuses on the thermomechanical behaviour. The paper begins with an overview of the fundamentals of thermoelastic and thermoplastic deformation in metal-ceramic composites. Various approaches, including the rule of mixture approximations, mean field theories, crystal plasticity models, discrete dislocation models, and continuum finite element formulations of the constitutive phases of the composites, are discussed, and the significance and limitations of these approaches are highlighted. Issues specific to the thermomechanical analyses of graded materials are then addressed. It is reasoned that the introduction of a new length scale to the problem due to compositional gradients inevitably calls for detailed micromechanical analyses of the size, shape, continuity, and spatial dispersions of the constituent phases of graded metal-ceramic composites. Models for the thermal, elastic, and plastic deformation of graded multilayers are then presented within the context of classic beam and plate theories, in conjunction with strategies for developing 'design diagrams' for thermomechanical performance. Methods to identify the conditions governing the onset of instability and abrupt shape changes due to large deformation in graded multilayers are also provided. The macroscopic continuum analyses are followed by discussions of micromechanics simulations of the real microstructural dispersions by recourse to computational models which invoke von Mises type and crystal plasticity theories. Experimental methods to assess the validity of such models are then examined, along with typical results of processing induced internal stresses and thermal stresses arising from temperature excursions in model systems with gradients in metal-ceramic concentrations. It is demonstrated that stepwise or continuously graded metal-ceramic composites can be designed to improve interfacial bonding between dissimilar solids, to minimise and optimally distribute thermal stresses, to suppress the onset of plastic yielding, to mitigate the deleterious effects of singular fields at free edges of multilayers where interfaces intersect free surfaces, to reduce the effective driving force for fracture, and to arrest cracks.