  In this paper we give a concept of multi-dimensional-time dynamical system
(MDTDS). Such dynamical system is generated by a finite family of functions
$\{f_i\}$. The multi-dimensional-time space is taken as a free group. Using the
subgroups of the free group we define periodic orbits of MDTDS and construct
such orbits. We study fixed points of MDTDS and show that the set of the fixed
points is the intersection of the set of fixed points of each $f_i$. The
$\omega$-limit set of the MDTDS is defined and some properties of the set is
studied. Moreover we construct a MDTDS for income of a deposit from several
banks and construct a MDTDS on circle. For these MDTDSs we describe the set of
fixed and periodic points. We discuss several open problems.
