Measurement of excited charm and charm-strange meson production with ZEUS at HERA The production of excited charm, D_1(2420)^0 and D_2^*(2460)^0, and charm-strange, D_s1(2536)+/-, mesons was measured with the ZEUS detector at HERA using an integrated luminosity of 126 pb^-1. The mesons were reconstructed in the D^*+ pi^-, D^+ pi^-, D^*+ K^0_s and D^0 K^+ (+c.c.) final states. The measured yields were used to determine the rates of c quarks hadronising as a given excited D meson and to the ratios of the dominant D_2^*(2460)^0 and D_s1(2536)+/- branching ratios. A search for the radially excited charm meson, D^*(2640)+/-, in the D^*+ pi^+ pi^- (+c.c.) final state was also performed. The results are compared with previous measurements and with theoretical expectations.