  We introduce the 2-colour parity. It is a theory of parity for a large class
of virtual links, defined using the interaction between orientations of the
link components and a certain type of colouring. The 2-colour parity is an
extension of the Gaussian parity, to which it reduces on virtual knots. We show
that the 2-colour parity descends to a parity on free links. We compare the
2-colour parity to other parity theories of virtual links, focusing on a theory
due to Im and Park. The 2-colour parity yields a strictly stronger invariant
than the Im-Park parity. We introduce an invariant, the 2-colour writhe, that
takes the form of a string of integers. The 2-colour writhe is a concordance
invariant, and so obstructs sliceness. It is also an obstruction to
amphichirality and chequerboard colourability within a concordance class.
