The authors use the possible-world approach to give the semantics of jumps and block expressions in ALGOL-like languages. The possible-world method is usually used to interpret modal and intuitionistic logics. The corresponding semantic technique was introduced by Reynolds and Oles. The authors develop this technique. The domains, environments, and valuation functions are parametrized by local aspects of the interpretation, namely by possible worlds. Domains and valuation functions for different possible worlds are not arbitrarily different from one another, and therefore they satisfy appropriate uniformity conditions. Consequently, the conventional semantic domains are generalized to functors from a category of possible worlds to a category of domains, and semantic valuations are generalized to natural transformations of such functors. In this generalized framework, the adequate notion of continuation is used to interpret block expressions and nonlocal jumps. A Hoare-like logic for reasoning about programs with jumps is defined. The logical approach is not entirely satisfactory; the reasoning about block expressions fails.