  We give an alternative proof of the theorem of Alikakos-Fusco [AF] concerning
existence of heteroclinic solutions to a Hamiltonian ODE system on the whole
real line which arises in the theory of phase transitions. Our method is
variational but differs from the original artificial constraint method of [AF]
and establishes existence by analysing the loss of compactness in minimising
sequences of the action in the appropriate functional space. Our assumptions
are slightly different from those considered previously and also imply a priori
estimates for the solution.
