It is shown that a WZW model corresponding to a general simple group p
ossesses in general different quantisations which are parametrised by
Hom(pi(1)(G), Hom(pi(1)(G), U(1))). The quantum theories are generical
ly neither monodromy nor modular invariant, but all the modular invari
ant theories of Felder et al. are contained among them. A formula for
the transformation of the Sugawara expression for L(0) under conjugati
on with respect to non-contractible loops in LG is derived. This formu
la is then used to analyse the monodromy properties of the various qua
ntisations. It turns out that for pi(1)(G) congruent to Z(N), With N e
ven, there are two monodromy invariant theories, one of which is modul
ar invariant, and for pi(1)(G) congruent to Z(2) x Z(2) there are eigh
t monodromy invariant theories, two of which are modular invariant. A
few specific examples are worked out in detail to illustrate the resul
ts.