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Hyper-heuristics are proposed as a higher level of abstraction as compared to the metaheuristics. Hyper-heuristic methods deploy a set of simple heuristics and use only non-problem-specific data, such as fitness change or heuristic execution time. A typical iteration of a hyper-heuristic algorithm consists of two phases: the heuristic selection method and move acceptance. In this paper, heuristic selection mechanisms and move acceptance criteria in hyper-heuristics are analyzed in depth. Seven heuristic selection methods and five acceptance criteria are implemented. The performance of each selection and acceptance mechanism pair is evaluated on 14 well-known benchmark functions and 21 exam timetabling problem instances.