The work is devoted to the solvability of local and nonlocal boundary-value problems for composite (Sobolev-type) equations \({D}_{t}^{2p+1}\left({D}_{t}^{2}-\Delta u\right)\) + Bu = f(x, t), where \({D}_{t}^{k}={\partial }^{k}/\partial {t}^{k}\) , Δ is the Laplace operator acting on spatial variables, B is a second-order differential operator that also acts on spatial variables, and p is a nonnegative integer. For these equations, the existence and uniqueness of regular solutions (possessing all generalized derivatives in the Sobolev sense that are involved in the equation) are proved to initial-boundary-value problems and the boundary-value problems nonlocal in the time variable. Some generalizations and refinements of the results obtained are also described.
