In this paper, a general method to establish the asymptotic behaviour of solutions to multi-order multiple time-varying delays nonlinear systems is proposed. The method, relying on vector Lyapunov-like functions and on comparison arguments, reduces the asymptotic stability problem to verify a Hurwitz property on a suitable matrix. Many results in integer order systems can be easily generalized to multi-order systems since the obtained conditions are order-independent. The latter fact is exploited to obtain robust results when the derivation order is uncertain. To establish the method, robust multi-order multiple time-varying delays linear positive systems are studied generalizing previous results existing in the literature. Two illustrative examples are presented, the main one providing conditions for asymptotic stability of a multi-agent multi-order system with time-varying delay. (C) 2019 Elsevier B.V. All rights reserved.