A generalised discrete torsion is a generalisation of the ordinary discrete torsion for suitable orbifold compactifications, where different local phases are allowed for different fixed points. Although these additional configurations give rise to modular invariant partition functions at one loop, their consistency at higher genera was still unclear. In this talk, I will present the construction of the T^6/Z2 x Z2 orbifold partition function at genus two, and I will discuss the constraints imposed by two-loop modular invariance on the local phases. This talk is based on a work in progress with Carlo Angelantonj and Diego Perugini.