In this note, we give a bound on the coupling time of an irreducible (max,plus) linear system $X(n) = A \otimes X(n-1)$ with its pseudo-periodic regime. This bounds uses a decomposition of the matrix $A$ into its critical part $A_c$ and its non-critical part $B$, as well as the maximal average weight of a circuit in $B$, which could be seen as the counterpart of the second largest eigenvalue in the classical linear case.