Bacteriophage Mu and many other transposable elements undergo transposition by a process that involves replication of the element. We describe here a mechanism by which such integrative replication may take place. We hve examined electron microscopically the DNA structures generated in host cells after Mu induction and have deduced the following steps in the transposition process, (i) Association. A protein-mediated association is brought about between the transposable element and the target DNA. (ii) Attachment. One end of the element is nicked and attached to a site that undergoes a double-stranded cleavage. (iii) Roll-in replication. While one strand of the target DNA is linked to the nicked strand of the element, the complementary strand of the target DNA is used as a primer for replication into the element such that the replicating DNA is threaded through the replication complex. (iv) Roll-in termination. When the distal end of the element arrives at the replication complex, replication is terminated. The roll-in replication mechanism can also explain laying down of tandem repeats--i.e., amplification of circular DNA sequences.