The paper describes problems related to the brand internationalisation and globalisation as one of the main marketing instruments used by a contemporary company. The brand is recognized not only as a product marking, but as a set of general associations and representations related to the product created and saved in the mind of customers. The process of creating the brand interpreted in such a way is referred to as market positioning. Building a strong international or global brand requires not only spending large sums of money but also choosing a positioning strategy that would take into account cultural, legal, economic and other differences, following the rule of “think globally, act locally”. By taking into account the above-mentioned determinants the researchers have assessed the suitability of particular brand positioning strategies in the global market and have pointed out their limitations and traps.