School systems in various European countries have been undergoing the process of decentralisation when the responsibility for education is being shifted from the central to the level of particular schools. This is true for the Czech Republic as well where schools are given more and more autonomy thus schools are fully becoming responsible for their work (this tendency is also highlighted in all of our development programmes on the state and regional level). This responsibility is shown also by accepting self-evaluation processes as internal part of the work of schools. However, self-evaluation is in fact new task for schools within our system and also a kind of "must" (reinforced since 1st January 2005 also by new the School Law when Schools are now expected to develop their own education programs whose part is internal evaluation). All this creates pressure on schools and on their head teachers as well - they have to deal with this situation. There are of course differences among schools though fear prevails for most of our teachers and head teachers, the fear from assessment or evaluation as such (in the past the evaluation in our country was linked with external evaluation only and negative findings were followed by sanctions). As perhaps not prevailing but very common way of learning of most of the heads is learning by doing nowadays (on the job) and school self-evaluation can be seen as challenge for our head teachers, we were deeply interested in their approach to this new situation.Our paper focuses not only on the description of the head teachers current situation, circumstances of their work but also on accurate finding the issues that Czech headmasters fear at most within this change. Establishing whether head teachers see any of their school strong points as their advantage or suggestions how they plan to solve this given situation (at the beginning of this whole processof implementing this change in particular) will be in the centre of our attention. This information will be gained from approximately 100 head teachers of primary and secondary schools. Respondents will be from various places in our country. Tools for gathering data will be questionnaires followed by discussions. In the questionnaires head teachers´ problems and expected complications regarding self-evaluation will be identified as well as their possible strong points. Following discussions will serve as a mean for finding out all the probable solutions of this situation and explaining their pros and cons. Suggestions based on experiences from particular European countries will also be one of our objectives in the research finding. We will also be looking for differences in head teachers´ opinions (if there are any), regarding the type of school they are from in particular and for any similarities with other head teachers´ opinions in particular countries.