The decentralized integral controllability (DIC) for linear/nonlinear square processes implies the existence of stable decentralized controllers with integral actions capable of achieving offset-free control and detuning any subset of the control loops independently. However, the current version of the DIC cannot be directly applied to nonsquare processes specifically for multiple-input single-output (MISO) processes. This paper presents the new definition and theorem of multiloop integral controllability (MIC) to nonlinear MISO processes, and proposes the sufficient MIC conditions in order for such processes to guarantee decentralized unconditional stability under control loop failure as well as to achieve offset-free tracking performance. Two examples, the quadruple-tank system (model based) and the temperature control system, are modified as two-input single-output (TISO) plants and given to quantitatively interpret the effectiveness of the proposed MIC analysis where the desirable performance of both applications can be obtained.