In this paper we analyze the dynamics of an R&D differential game allowing for

technological spillovers and sigmoid learning functions of multiproduct oligopolies.

We demonstrate how the presence of learning together with spillovers may generate

a rich set of outcomes, varying from constant leadership to catching-up and falling

behind as well as from technology lock-in to a situation with a large number of high

quality products. These types of outcomes are qualitatively different both from the

single firm dynamics with learning and from the duopoly case with spillovers and

without learning.