Abstract
A formalism based on quaternionic Hilbert spaces is developed to describe the coloured hadron states. The definition of the multi-particle states consistent with the quaternionic structure is given. This definition implies the selection rules equivalent to the colour confinement. It is found that for the symmetry group G=GF*SU(3) this theory is algebraically equivalent to the Fritzsch and Gell-Mann model (1973).