Cross-border activities of European companies, including insurance undertakings, constitute the major component of EU legal system. The freedom of establishment and the freedom to provide services rules are the crucial foundations of the single internal market, as they enable EU entrepreneurs to take up and pursue economic activity in the territory of another Member State. Unfortunately, the EU market has its weaknesses, one of which has been recently experienced by the Polish insurance market. This is due to the lack of a uniform guarantee system which would coherently deal with the issues related to the European insurer’s insolvency and, above all, to the settlement of claims of entitled persons and to the payment or refund of benefits, which has particular consequences for entitled persons holding motor third-party liability insurance, being the most popular insurance product.Given the above, the performance of the Polish Insurance Guarantee Fund is of the utmost importance. The legislator has failed to precisely regulate several issues related to the organisational aspects of the institution’s activities of in the event of bankruptcy or compulsory liquidation of an insurance company operating in Poland on a cross-border basis. Therefore, some demands for amendments to the Compulsory Insurance Act have been presented. The most urgent demand, however, is about providing for unambiguous method for determining which Member State’s guarantee scheme should satisfy the claims of entitled persons, i.e. whether it should be the scheme of the insolvent or bankrupt insurer’s home Member State or rather the scheme of the Member State where it conducted its cross-border operations. Besides, the determination of the mode of reimbursement by the guarantee scheme of the insolvent or bankrupt insurer’s country of origin will increase the level of responsibility of supervisory institutions of that country for the operation of entities subject to their supervision and conducting cross-border business.