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This approach addresses an adaptive-sliding-mode guidance law for missiles equipped with thrust vector control and divert control system, for the task of intercepting of a theatre ballistic missile with manoeuvring acceleration. The aim of the present study is to achieve a bounded target interception under the three degrees of freedom (DOF) control and the zero-effort-miss phase to improve the intercepting accuracy of the missile by narrowing the distance between the intercepting missile and the target missile to within effective range for triggering the missile's explosion. Considering the external disturbances and the variation in the missile's mass, the 3 DOF adaptive-sliding-mode guidance law is designed using adaptive control and sliding-mode control to minimise the distance between the centre of the intercepting missile and that of the target missile asymptotically. Also, the overall system stability is verified using the Lyapunov stability theory. Furthermore, successful simulation results are conducted to validate the effectiveness of the proposed adaptive-sliding-mode guidance law.