The interaction of two propagating vortex pairs is considered, each pair being initially aligned along the positive principal axis of strain associated with the other. As a preliminary, the action of accelerating strain on a Burgers vortex is considered and the conditions for a finite-time singularity (or ‘blow-up’) are determined. The asymptotic high Reynolds number behaviour of such a vortex under non-axisymmetric strain, and the corresponding behaviour of a vortex pair, are described. This leads naturally to consideration of the interaction of the two vortex pairs, and identifies a mechanism by which blow-up may occur through self-similar evolution in an interaction zone where scale decreases in proportion to (t* − t)1/2, where t* is the singularity time. The relevance of Leray scaling in this interaction zone is discussed.