Abstract The paper proposes two new methods for analyzing case and adposition meaning. The method for analyzing case and adposition semantics is based on an analysis of semes (semantic components) as arguments and predicates in a higher-order logic. The method for case and adposition pragmatics is based on an analysis of case and adposition functions as a series of functional derivations. The methods are complementary, cross-linguistically universal and allow for cross-category generalizations. A thorough discussion of the methods (including comparisons with earlier ones), formal definitions of case/adposition meanings and a variety of examples are provided.