A countably infinite class of multimode q-oscillator algebrasA k;m (k = 1, 2, ...,∞ m = 1, 2, ...) is obtained with the aid of the R-matrix method in quantumgroup theory for q 2(k+1) = 1. The related Fock spaces are given and they showthat the q-particle systems described by A k;m obey a generalized Pauli exclusionprinciple. The algebras A k;m are represented on a kind of q-holomorphic functionspaces B(¯η) k;m which are generalizations of the usual Bargmann–Fock spaceswith many Grassmann variables and have Hilbert space structures with the scalarproduct given by an algebraically defined integral. When taking k = 1 or k →∞, all of the above are reduced to the corresponding results for the usual multimodefermion and boson systems, respectively.