  In this paper, we analyze the modification of integrable models in the
$\kappa$-deformed space-time. We show that two dimensional isotropic oscillator
problem, Kepler problem and MICZ-Kepler problem in $\kappa$-deformed space-time
admit integrals of motion as in the commutative space. We also show that the
duality equivalence between $\kappa$-deformed Kepler problem and
$\kappa$-deformed two-dimensional isotropic oscillator explicitly, by deriving
Bohlin-Sundman transformation which maps these two systems. These results are
valid to all orders the the deformation parameter.
