Different local features at the surface of a body are breaks or sharp changes in boundary conditions, separation or joining of a flow, irregularities, etc., and they may have a marked effect on local and global characteristics of flow over it [1]. This situation stimulates continued interest towards to flow in local regions, which apart from considerable practical importance, often exhibit considerable theoretical novelty (see, e.g., [2–6], where a systematic study was carried out of planar local regions of flow). However, the majority of local regions are spatial, and whereas in studying flat regions considerable success have been achieved, for spatial regions only individual solutions have been obtained, often using considerable simplifications [7–19]. In addition, due to the absence of systematic studies it is difficult to determine the boundaries for existence of different flow regimes in local spatial regions, and limiting transitions which make it possible to changeover from one flow regime to another. In this work systematic studies are carried out for flow regimes in local spatial regions for each of the boundary problems formulated, the main properties of their solution are studied, and a general classification for the arrangement of flow regimes is built up.