The article aims at an analysis of the systemic position of the head of state, as set in the wide formula of the Parliamentary system, and of the function of the political arbitrate attributed to the head of state. It begins with a general observation that, in the case of a head of state in a parliamentary regime, the so called 'arbitrage function' is obligatory. In such a system of governance, the monarch or the president is not expected to be the leader of the executive, a factor ruling in the full meaning of the term. Quite to the contrary; in accordance with such principles of traditional Parliamentarism as 'the King can do no wrong', 'the King may not act on his own', and, lastly, 'the King reigns but he does not govern', in a Parliamentary system the head of state is moved aside, performs ceremonial functions, is a figurehead or, as the tale in the III French Republic held, is a person who cuts the ribbons at flower exhibitions. Apart from performing his representative and ceremonial entitlement, a president (a monarch) also exercises political arbitrage. The latter may take very different forms. It may be, e.g. a sport arbitrage, where the head of state is expected only to observe the rules of the game. It may be also a judicial arbitrage, where, apart from legality, the assessment of the arbiter may also be based on being right and fair. It may, finally, be arbitrage in the sense of making decisions, dangerously approaching the concept of arbitrariness, where the arbiter's actions mean a specific right to a 'free hand'; that is, the right to take decisions which are the best in the arbiter's opinion. Apart from this, the arbitrage of the head of state may take the form of value arbitrage, where the arbiter will protect those values significant to the state and its system. A so-called party arbitrage may be also indicated; this assumes that the head of state has an active role in maintaining the ruling coalitions, and, if necessary, in seeking the parliamentary majority providing a base for the government. However, whatever the type of arbitrage and whether it genuinely comes to the fore in practice or not, the arbitrage (a function of political arbitrage) is recognised as a necessary component of the structure of parliamentary governments.