The authors establish dynamical localization properties of certain families of unitary random operators, called unitary Anderson model, on the \(d\)-dimensional lattice in various regimes. For the unitary Anderson model one choose a unitary operator on \(l^2(\mathbb{Z}^d)\) of the form \(U_\omega=D_\omega S\), where S is a deterministic unitary operator and \(D_\omega\) a multiplication operator by random phases, i.e., for every \(\phi\in l^2(\mathbb Z^d)\) and \(k\in\mathbb Z^d,\)
\[ (D_\omega\phi)(k)=\exp(-i\theta^\omega_k)\phi(k), \]
with i.i.d. random phases \(\theta^\omega_k\) taking values in \(T:=\mathbb{R}/2\pi \mathbb{Z}.\) It is proved that an exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization.