The loss of superhelical turns from a covalently closed duplex DNA exposed to bacteriophage T4 DNA ligase in the presence of AMP and Mg2+ has recently been found to be gradual and not sudden (Montecucco, A. and Ciarrocchi, G. (1988) Nucleic Acids Res. 16, 7369-7381). In this paper, we show that the AMP-dependent DNA relaxation catalyzed by human and E. coli DNA ligases also takes place according to a step-wise mechanism. DNA relaxation is inhibited by pyrophosphate, by ATP (or NAD in the case of the E. coli enzyme) and by high ionic strength and is essentially distributive with the human or T4 DNA ligases, and processive with the bacterial one. The AMP-dependent ability of DNA ligases to relax DNA might allow these enzymes to relieve possible topological complications of the nascent double helix generated by the replication of the lagging strand.