We introduce the vector meson contributions in heavy-light chiral pert
urbation theory (HLCPT) and construct the Lagrangian and current to th
e order 1/m(Q). With this, to the order 1/Lambda(csb)(2) (Lambda(csb)
is the chiral symmetry breaking scale) we calculate corrections to f(D
) and f(B) arising from coupled-channel effects to the orders 1/m(c) a
nd 1/m(b). At the tree level in HLCPT, using the relativistic Bethe-Sa
lpeter (BS) equation with the kernel containing a confinement term and
a gluon exchange term in a covariant generalization of the Coulomb ga
uge we calculate f(D)((0)) and f(B)((0)) when m(Q) --> infinity as wel
l as the 1/m(Q) corrections. HLCPT and the heavy quark effective theor
y (HQET) are matched at the scale Lambda(csb). Adding the perturbative
and nonperturbative contributions we give the values for f(D) and f(B
) respectively. It is found that our result is in agreement with the r
elation f(D) = f(B) from lattice calculations.