Using data collected with the LHCb detector in proton-proton collisions at a centre-of-mass energy of 7 TeV, the semileptonic decays (B) over bar (0)(s) -> D+X mu(-)(nu) over bar and (B) over bar (0)(s) -> (DK+X)-K-0 mu(-)(nu) over bar are detected. Two structures are observed in the (DK+)-K-0 mass spectrum at masses consistent with the known D-s1(2536)(+) and D-s2*(2573)(+) mesons. The measured branching fractions relative to the total (B) over bar (0)(s) semileptonic rate are B((B) over bar (0)(s) -> (Ds2X)-X-*mu(-)(nu) over bar /B(B-2(-0) -> X mu(-)(nu) over bar) = (3.3 +/- 1.0 +/- 0.4)%, and B((B) over bar (0)(s) -> (Ds2X)-X-*mu(-)(nu) over bar /B(B-2(-0) -> X mu(-)(nu) over bar) = (5.4 +/- 1.2 +/- 0.5)%, where the first uncertainty is statistical and the second is systematic. This is the first observation of the D-s2*(+) state in B-s2*(+) decays; we also measure its mass and width. (C) 2011 CERN. Published by Elsevier B.V. All rights reserved.