We study the online version of the scheduling problem Q∥Cmax involving selfish agents, considered by Archer and Tardos in [A. Archer, E. Tardos, Truthful mechanisms for one-parameter agents, in: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS), 2001, pp. 482–491], where jobs must be scheduled on m related machines, each of them owned by a different selfish agent.We present a general technique for transforming competitive online algorithms for Q∥Cmax into truthful online mechanisms with a small loss of competitiveness.We also investigate the issue of designing new online algorithms from scratch so as to obtain efficient competitive mechanisms, and prove some lower bounds on a class of “natural” algorithms. A “direct” use of such natural algorithms to construct truthful mechanisms yields only trivial upper bounds for the case of two machines.Finally, we consider mechanisms with verification, introduced by Nisan and Ronen [N. Nisan, A. Ronen, Algorithmic mechanism design, in: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, STOC, 1999, pp. 129–140], for offline scheduling problems. We present the first constant-competitive online truthful mechanism with verification for any number of machines.