In this paper we study Markov-perfect equilibria (MPE) of two-player multimode

dierential games with controlled state dynamics, where one player controls

the transition between modes. Different types of MPE are characterized distinguishing

between delay equilbria, inducing for some initial conditions mode switches

after a positive finite delay, and now or never equilbria, under which, depending on

the initial condition, a mode switch occurs immediately or never. These results are

applied to analyze the MPE of a game capturing the dynamic interaction between

two incumbent firms among which one has to decide when to extend its product

range by introducing a new product. The market appeal of the new product can

be (positively or negatively) in

uenced over time by the competing firms through

costly investments. It is shown that under a wide range of market introduction costs

a now or never equilibrium co-exists with a continuum of delay equilibria, with each

of them inducing a different time of product introduction.