Globalization of business, promotion of economic interests to the markets of other countries, processes of unification and creation of common economic space require knowledge of national customs and national culture. Culture is, first of all, predictability. The ability to understand and use the features of national cultures, interpersonal communications and business ethics in global business is an important task of cross-cultural management. The success of international companies in Europe in providing high quality products and services depends, on the one hand, on the dynamics of the growing economic environment and, on the other hand, on the adoption of global quality standards and procedures. As the European market becomes more and more global, the products and services offered by international companies around the world face the challenges of a multicultural environment, not only at the level of customer relations, but also deep inside the companies, at the level of employees. The article describes the characteristics of cross-cultural management of enterprises in the European markets, identifies the barriers to its implementation, and considers the most effective solutions in the field of cross-cultural personnel management. Cross-cultural management of enterprises in the European markets is, first of all, the creation and application of technologies for managing cultural diversity in the context of globalization, which successfully operate in different cultures, prevention of intercultural conflicts. As a solution, the development of intercultural competencies, training of global managers in Europe in key aspects of intercultural interaction, introduction and active use of advanced digital technologies, as well as building a management system are proposed. Knowledge management provides the necessary technological support for cross-cultural management of European enterprises to improve knowledge sharing, their effective use in the activities of multinational companies and international joint ventures in Europe.