  The masses of excited heavy mesons are studied with sum rules in the heavy
quark effective theory. A set of interpolating currents creating (annihilating)
excited heavy mesons with arbitrary spin and parity are proposed and their
properties are discussed. Numerical results at the leading order of the {\cal
O}(1/m_Q) expansion are obtained for the lowest doublets (0^+, 1^+) and (1^+,
2^+).
