The spectrum of the 0(++), 0(--), 1(-+), and 1(+-) heavy-light hybrids are
calculated in HQET. The interpolated currents of the hybrids are chosen as
<g(q)over bar gamma>(alpha)G(alpha mu)(a)Th(upsilon)(x), <g(q)over bar gamm
a>(alpha)gamma(5)G(alpha mu)(a)T(a)h(upsilon)(x), and <g(q)over bar sigma>(
mu alpha)G(alpha mu)(a)T(a)h(upsilon)(x). Some strong couplings and decay w
idths of the heavy-light hybrids to B(D) pi are calculated by using QCD sum
rules. The masses of 0(++) hybrids with a gluon in TM(1(--)) and TE(1(+-))
modes are found to be similar, while the decay widths of them are found to
be different. A two-point correlation function between the pion and vacuum
is employed and the leading order of 1/M-Q expansion is kept in our calcul
ation.