It has been proved in [12]that properties of graphs or other relational structures that are definable in first-order logic can be decided in linear time when the input structures are restricted to come from a locally tree-decomposable class of structures. Examples of such classes are the class of planar graphs or classes of graphs of bounded degree. In this paper, we consider more general computational problems than decision problems. We prove that construction, listing, and counting problems definable in first-order logic can be solved in linear time on locally tree-decomposable classes of structures.