Branch and bound (BB) is the primary deterministic approach that has been applied successfully to solve mixed-integer nonlinear programming (MINLPs) problems in which the participating functions are nonconvex. Recently, a decomposition algorithm was proposed to solve nonconvex MINLPs. In this work, a generalized branch and cut (GBC) algorithm is proposed and it is shown that both decomposition and BE algorithms are specific instances of the GBC algorithm with a certain set of heuristics. This provides a unified framework for comparing BE and decomposition algorithms. Finally, a set of heuristics which may be potentially more efficient computationally compared to all currently available deterministic algorithms is presented.