Quaternion generalized fiber bundles {Mathematical expression} are studied, both isomorphic to global tensorial product {Mathematical expression} ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class {Mathematical expression} is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a splitting principle are proved for bundles {Mathematical expression}. On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which e{open}( {Mathematical expression}=e{open}(BE)) relations are stated among Stiefel-Whitney classes of {Mathematical expression}, BE and the class e{open}. © 1975 Fondazione Annali di Matematica Pura ed Applicata.