This paper aims to explore the factors influencing the ability of firms to compete in globalised markets. The Austrian and evolutionary economics and the endogeneous growth literature highlight the role of innovation activities in enabling firms to compete more effectively - and expand their market share. On the basis of these theories, and using a large panel of firms from several Central and East European Countries (CEECs), this paper attempts to identify the factors and forces which determine the ability of firms to compete in conditions of transition. The competitiveness of firms, measured by their market share, is postulated to depend on indicators of firms' innovation behaviour such as improvements in cost-efficiency, labour productivity and investment in new machinery and equipment as well as characteristics of firms and their environment such as location, experience, technological intensity of their industries and the intensity of competition. To control for the dynamic nature of competitiveness and the potential endogeneity of its determinants, and to distinguish between short and long run effects of firm behaviour, a dynamic panel methodology is employed. The results indicate that the competitiveness of firms in transition economies is enhanced with improvements in their cost efficiency, productivity of labour, investment and their previous business experience while stronger competition has a negative impact on it.