The knowledge innovation process can be defined as consisting of two sub-processes, knowledge production process and knowledge commercialization process.　Those two sub-processes are supposed to have proper inputs and outputs and they are linked together by technological innovations (patents).　In the article, the innovation efficiency of knowledge innovation process and its two sub-processes is measured by DEA modelling (data envelopment analysis) in the period of 2004-2010. Altogether, 19 countries of the European Union are studied, with a particular focus on the efficiency of innovation processes in the Visegrad countries which joined the EU in the same year 2004.　Financial system is one of the major factors which determine the innovative activities of actors.　The aim of article is to uncover slacks (surpluses) on the input and output side of knowledge processes.　It can be supposed that the largest slacks exist on the side of the financial support in relation to produced innovative outputs.　The DEA method shows that majority of countries reach higher relative innovation efficiency in knowledge commercialization than in knowledge production and the most important slacks can be found in financing of research and development.　Findings also suggest that although the efficiency of innovation processes would have been expected higher in the old EU member countries, their efficiency is lower than in some of the Visegrad countries.　The reason may be the ability of the Visegrad countries to generate relatively satisfactory outputs from low inputs compared with other countries.　Surprisingly, they are also in a group of high performers in bringing innovations to market, although they show substantial deficiencies in generating patents and papers. JEL Classification: O340