Innovation activities in the German enterprise sector showed two opposing trends over the past two decades: While total innovation expenditures grew substantially, the number of firms conducting innovation activities fell sharply. Innovation expenditures hence concentrate on fewer firms. In this paper we analyse the evolution of firms' innovation and R&D activities. Based on panel data from the German part of the Community Innovation Survey covering a 13 years period (2001 to 2013) we use continuous-time Markov-Chains to analyse the changing properties of the firms' choices to conduct R&D and non-R&D innovation activities. Our findings are threefold. As compared to the pre-crisis period 2001-2007 there is a considerable change in innovation and R&D behaviour of German firms from 2008 onwards with an increasing number of firms exiting R&D and innovation activities. Smaller firms are the main driver behind this process, particularly with regard to quitting non-R&D innovation activities. Although smaller firms were also less likely to move to higher levels of innovativeness and R&D engagement and more likely to fall back in the pre-crisis period, these trends have been more pronounced in the crisis and even in the post-crisis period. Both public innovation support and better financial capabilities can increase the rate chances to move to higher levels of innovativeness and reduce the chances to fall back.