We consider a discrete-time two-dimensional process {(X1,n,X2,n)} on Z+2 with a supplemental process {Jn} on a finite set, where the individual processes {X1,n} and {X2,n} are both skip-free. We assume that the joint process {Yn}={(X1,n,X2,n,Jn)} is Markovian and that the transition probabilities of the two-dimensional process {(X1,n,X2,n)} are modulated depending on the state of the supplemental process {Jn}. This modulation is space homogeneous except for the boundaries of Z+2. We call this process a discrete-time two-dimensional quasi-birth-and-death process. Under several conditions, we obtain the exact asymptotic formulae of the stationary distribution in the coordinate directions. [ABSTRACT FROM AUTHOR]