A careful study of the existence of exotic states in two-dimensional gauge theories with SU( M)-flavour and diagonal SU( N)-colour symmetry is made using non-perturbative operator techniques. Special care is given to the interpretation of these exotic states which in general are shown to possess non-conventional properties. Except for a very special “θ-world”, the SU( N) torus case is found to exhibit two different phases characterized by the presence and absence of exotic states, respectively. No such phase transition is observed in the case of SU( M) flavour.