This paper deals with the problem of linearisation of systems with constant commensurable delays by input-output injection using algebraic control tools based on the theory of non-commutative rings. Solutions for the problem of linearisation free of delays, and with delays of an observable nonlinear time-delay systems are presented based on the analysis of the input-output equation. These results are achieved by means of constructive algorithms that use the nth derivative of the output expressed in terms of the state-space variables instead of the explicit computation of the input-output representation of the system. Necessary and sufficient conditions are established in both cases by means of an invertible change of coordinates.