A review of the current state of the quasinuclear quark model and of its application to hadronhadron and hadron-nucleus collisions at high energies is presented. Particular attention is devoted to multiple production of secondary particles. It is shown that such processes can be used as a basis for a detailed verification of the hypotheses of quark additivity and quark statistics. Comparison of calculations performed in this model with experimental data provides information on the quark hadronization mechanism.