Abstract. Recently observed charmed mesons, D * 1 (2760), D * 3 (2760) and charmed-strange mesons, D * s1 (2860), D * s3 (2860), by BaBar and LHCb collaborations are considered to be plausible candidates for cq 1 3 D J (q = u, d, s) states. We calculate the strong decays with one pion (kaon) emission of these states including well-established 1S and 1P charmed(-strange) mesons within the framework of the covariant oscillator quark model. The results obtained are compared with the experimental data and the typical nonrelativistic quark-model calculations. Concerning the results for 1S and 1P states, we find that, thanks to the relativistic effects of decay form factors, our model parameters take reasonable values, though our relativistic approach and the nonrelativistic quark model give similar decay widths in agreement with experiment. While the results obtained for 1 3 D J=1,3 states are roughly consistent with the present data, they should be checked by the future precise measurement.