<p>A discrete analog of the classical van der Pol oscillator is studied. For an individual oscillator, we present charts of dynamical regimes and Lyapunov exponent charts depending on the excitation parameter and discretization parameter. For two dissipatively coupled oscillators, the structure of plane “frequency detuning –magnitude of the coupling” for different values of the discretization parameter is examined. The analogies and differences in comparison with the original flow system are discussed. In a discrete system, we observe the arising of resonant two-frequency quasi-periodic regimes tongues embedded in the three-frequency domain. We study their internal structure, namely bifurcations of tori doubling, quasi-periodic shrimp-shaped domains and the transition to chaos. Taking into account the additional Duffing oscillator type nonlinearity leads to the emergence of Arnold resonance web. The case of the repulsive coupling of oscillators is also examined. It leads to the disappearance of a stable state equilibrium, which is replaced by a set of expanding quasi-periodic tongues. Inside them, shrimp-shaped domains emerge even with a small value of the discretization parameter.</p>