This paper deals with, by using the matrix fractional description (MFD) approach, the problem of feedback practical stabilization of nD (multidimensional) discrete systems whose input and output signals are unbounded in, at most, one dimension. A constructive algorithm is first presented for solving the Bezout equation over the ring of practically stable rational functions. Then, a necessary and sufficient condition for an nD system to be practically stabilizable is derived and the parameterization of all nD practically stabilizing compensators is given. These results make it clear that the nD practical stabilization problem can be essentially solved by using 1D approaches.