[en] If the exact gauge symmetry of nature consists of the U(1)sub(EM) generated by the electric charge operator Q and the colour group K, with Q a colour singlet, then, if g is a possible magnetic charge, exp(4πigQ) must equal an element of the colour group. For colour singlet particles this reduces to Dirac's condition eg = n/2. In general, possible monopoles correspond to points of intersection of the colour and electromagnetic groups. If the colour group is semi-simple and compact, there can at most be a finite number p of such points (p = N if K = SU(N)). The existence of non-trivial (not equal to unity) solutions to our condition means that there must be fractionally charged (with p the fraction) coloured particles and magnetic monopoles emanating colour magnetic flux as well as electromagnetic flux. (Auth.)