The focus of our research is the internationalisation of the small-medium size family firms in Hungary, with particular attention to the effect of generational change on internationalisation. Our examination is based on interviews with the current management of six family firms from different industries. We had two research propositions: First, we analysed if and how successors in the family businesses were more open to the internationalisation of the company. Our results provide insights reflecting that the predecessors are usually quite open, and successors are not always as open when they assume control over the company, unlike the existing internationalisation patterns of family firms would suggest. Potential explanations reveal related characteristics of the Central-Eastern European (CEE) region. Secondly, in terms of how and why the leadership style and approach of the predecessors affect the internationalisation of family firms, our findings from different cases vary. The historical and cultural background of the family firms' founders and early-generation successors exert notable influence on the internationalisation process, while the role of predecessors' personal characteristics may not be as strong a driver of internationalisation as previously suggested. The management implications of our findings suggest that the Hungarian family firms show regional patterns in terms of their internationalisation, and generic approaches to generational change and succession may not explain the process as much as extant literature on international family business suggests.