The PHENIX experiment at the Relativistic Heavy Ion Collider has performed a systematic study of K0S and K*0 meson production at midrapidity in p+p, d+Au, and Cu+Cu collisions at sqrt SNN = 200 GeV. The K0S and K*0 mesons are reconstructed via their K0S and [pi]0(2!gamma][gamma])[pi]0 (2!gamma][gamma]) and K*0 2!K "[pi]" decay modes, respectively. The measured transverse-momentum spectra are used to determine the nuclear modification factor of K0S and K*0 mesons in d+Au and Cu+Cu collisions at different centralities. In the d+Au collisions, the nuclear modification factor of K0S and K*0 mesons is almost constant as a function of transverse momentum and is consistent with unity showing that cold-nuclear-matter effects do not play a significant role in the measured kinematic range. In Cu+Cu collisions, within the uncertainties no nuclear modification is registered in peripheral collisions. In central collisions, both mesons show suppression relative to the expectations from the p+p yield scaled by the number of binary nucleon-nucleon collisions in the Cu+Cu system. In the pT range 2-5 GeV/c, the strange mesons (K0S, K*0) similarly to the.