A systematic method for quantitative characterisation of the topological properties of two-phase materials has been developed, which offers an effective way for the characterisation of twophase materials. In particular, a topological transformation has been proposed, which allows a two-phase microstructure with any grain size, grain shape and phase distribution to be transformed into a three-microstructural-element body (3-E body). It has been shown that the transformed 3·E body is mechanically equivalent along the aligned direction with the original microstructure. The Hall·Petch relation developed originally for single-phase metals and alloys has been successfully extended to two~ductile-phase alloys. It has been shown that the extended Hall- Petch relation can separate the individual contribution to the overall efficiency of different kinds of boundaries as obstacles to dislocation motion. A new approach to deformation behaviour of two-ductile-phase alloys has been developed based on Eshelby's continuum transformation theory and the microstructural characterisation developed in this thesis. In contrast to the existing theories of plastic deformation, this approach can consider the effect of microstructural parameters, such as volume fraction, grain size, grain shape and phase distribution. In particular, the interactions between particles of the same phase have also been taken into account by the topological transformation. Consequently, the newly developed theory can be applied in principle to a composite with any volume fraction. This approach has been applied to various two-ductile-phase alloys to predict the true stress·true strain curves, the internal stresses and the in situ stress and plastic strain distribution in each microstructural element. It is found that the theoretical predictions are in very good agreement with the experimental results drawn from the literature. A new approach has also been developed for the prediction of the Young's moduli of particulate two-phase composites. Applications of this approach to AVSiCp and Co/WCp composite systems and polymeric matrix composites have shown that the present approach is superior to both the Hashin and Shtrikman's bounds and the mean field theory in terms of the good agreement between the theoretical predictions and the experimental results from the literature. Furthermore, this approach can be extended to predict the Young's moduli of multiphase composites by iteration. This iteration approach has been tested on some Ti-6Al- 4V-TiB composites. An experimental investigation has being carried out to study the in situ Ti-6AI-4V-TiB (hereafter, Ti/TiB is used for convenience) metal matrix composites produced through a rapid solidification route. Production of in situ Ti/fiB metal matrix composites through rapid solidification route can completely exclude problems such as wetting and chemical reaction encountered by alternative production routes. The relevant microstructural phenomena in in situ Ti/TiB metal matrix composites, such as the growth habit of TiB phase and the w-phase transformation, have also been investigated. The TiB phase in the consolidated composites exhibits two distinguished morphologies: needle-shaped TiB and nearly equiaxed TiB. The needle-shaped TiB phase formed mainly from the solidification process always grows along the [010] direction of the B27 unit cell, leaving the cross-section of the needles consistently enclosed either by (100) and {101 1 type planes or by (100) and {102l type planes. It is also found that the cross-sections of the nearlyequiaxed TiB particles formed from the B supersaturated Ti solid solution are also bounded by the same planes as above, although the growth rate along the [010] direction has been considerably reduced. Experiments have also been perfonned to investigate the effect of pre-hipping heat treatments on the microstructure of RS products. It is found that pre-hipping heat treatments at a temperature below 800°C can lead to the precipitation of fine equiaxed TiB particles from the B super-saturated Ti solid solution, which are uniformly distributed throughout the a+B matrix. The majority of those TiB precipitates do not grow up by Ostwald ripening process after long time exposure at higher temperature. Microstructural examination has confirmed the existence of a B to w transformation in RS Ti- 6AI-4V alloys with and without B addition after consolidation. In addition, the B to w transformation has also been observed in RS Ti-Mn-B alloys after consolidation. Systematic electron diffraction work on the B-phase offers a strong experimental evidence for the B to W transformation mechanism proposed by Williams et al.