  We study the problem of two interacting particles in a two-dimensional
quasiperiodic potential of the Harper model. We consider an amplitude of the
quasiperiodic potential such that in absence of interactions all eigenstates
are exponentially localized while the two interacting particles are delocalized
showing anomalous subdiffusive spreading over the lattice with the spreading
exponent $b \approx 0.5$ instead of a usual diffusion with $b=1$. This
spreading is stronger than in the case of a correlated disorder potential with
a one particle localization length as for the quasiperiodic potential. At the
same time we do not find signatures of ballistic FIKS pairs existing for two
interacting particles in the one-dimensional Harper model.
