A plant is strongly stabilizable if there exists a stable compensator to stabilize it. Based on some theorems in complex analysis of several variables proved in this paper, we present necessary conditions for the strong stabilizability of complex and real n-D multi-input multi-output (MIMO) shift-invariant linear plants. For the real case, the condition is a generalization of the parity interlacing property of Youla, Bongiorno, and Lu [Automatica J. IFAC, 10 (1974), pp. 159-173] for the strong stabilizability of a real one-dimensional MIMO plant. These conditions are also sufficient for the cases of n-D plants with a single output (MISO) or with a single input (SIMO). For general n-D MIMO plants, we do not know if the conditions are sufficient or not. A useful sufficient, but not necessary, condition for the strong stabilizability of a class of n-D (n greater than or equal to 2) MIMO plants is given.