  Studies in string theory and quantum gravity lead to the Generalized
Uncertainty Principle (GUP) and suggest the existence of a fundamental minimal
length which, as was established, can be obtained within the deformed
Heisenberg algebra. The first look on the classical motion of bodies in a space
with corresponding deformed Poisson brackets in a uniform gravitational field
can give an impression that bodies of different mass fall in different ways and
thus the equivalence principle is violated. Analyzing the kinetic energy of a
composite body we find that the motion of its center of mass in the deformed
space depends on some effective parameter of deformation. It gives a
possibility to recover the equivalence principle in the space with deformed
Poisson brackets. and thus GUP is reconciled with the equivalence principle. We
also show that the independence of kinetic energy on composition leads to the
recovering of the equivalence principle in the space with deformed Poisson
brackets.
