In this work we study the supermanoeuvrability of a biomimetic morphing-wing case study aircraft system. Analytical and computational models of biomimetic flight dynamics are developed, utilising multibody dynamics, computational fluid dynamics, and reduced-order aerodynamic models; and validated with respect to experimentally-derived flight dynamics of a Pioneer RQ-2 UAV. These models are used to explore the capability of this system for a wide range of biological and other supermanoeuvres: multi-axis quasistatic nose-pointing-and-shooting (NPAS)/direct force capability; multi-axis rapid-nose-pointing-and-shooting (RaNPAS) including Pugachev's cobra; ballistic transition; and anchor turning. Novel contributions include the development of transient aerodynamic models for a three-dimensional flight-simulation context; the development of novel methods for assessing transient model validity; the development of improved methods of quaternion variational integration; the development of quasi-trim and continuation-based methods for the design, exploration, analysis and control of manoeuvres in biomimetic morphing-wing systems; an assessment of the complex spiral mode stability effects present in asymmetrically-morphed system trim states; and a demonstration of the wide-ranging potential for advanced supermanoeuvrability in biomimetic morphing-wing systems. Industrial applications include the design of high-precision guided missiles for use in complex, e.g. urban, environments.