Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and (...) there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point. We also describe a similar construction where we assume the existence of two classes consisting of rooted frames only. Using those classes and frames with so-called -roots, we construct a rooted frame adequate for the fusion of modal logics characterised by the classes under consideration. Both constructions can be used interchangeably. The selection of the construction depends on... (shrink)