The study provides reliable and comprehensive information for both practitioners and academics. The results revealed that museum visitors are demanding customers with very high expectations. Although the Krapina Neanderthal Museum delivered highly rated perceived service quality, the gap analysis showed that only one attribute of museum service quality (“audio guides provided”) was perceived significantly better than it was expected to be. In addition, service attributes representing helpful and courteous staff, tolerable level of crowding, convenient opening hours, informative, educational and attractive exhibition, new technologies that make the visit more interesting and the appearance of the museum building were assessed in accordance with the visitors’ expectations. These represent the strong points of the museum offerthat should be maintained in the future as well.