The masses of excited heavy mesons are studied with sum rules in the h
eavy 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 O(1/m(Q)) expansion are obtained for the lowest
doublets (0(+),1(+)) and (1(+),2(+)).