We report a study of the structure-processing-property relationships in a high strength Al93Fe3Cr2Ti2 nano-quasicrystalline alloy and composites containing 10 and 20 vol% ductilising pure Al fibres. The superimposed contributions of several different strengthening mechanisms have been modelled analytically using data obtained from systematic characterisation of the monolithic alloy bar. An observed yield strength of 544 MPa has been substantiated from a combination of solid solution strengthening, work hardening, precipitation hardening and Hall-Petch grain size dependent effects. These materials have been shown by other authors in previous published work to be highly sensitive to the size distribution of particles in the powder from which they are made, and the subsequent thermomechanical processing conditions. The processing condition employed in this study provided micron-sized grains with a strong [111] preferential orientation along the extrusion direction and a bimodal size distribution of the icosahedral nano-quasicrystalline precipitates. Both were deemed to be a significant contributor to the high yield strength observed. The addition of pure Al fibres was found to decrease the yield strength linearly with increasing Al content, and to augment the ductility of the composites.