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In the heavy quark effective theory, hadronic matrix elements of currentsbetween two hadrons containing a heavy quark are expanded in inverse powers ofthe heavy quark masses, with coefficients that are functions of the kinematicvariable $v\cdot v'$. For the ground state pseudoscalar and vector mesons, thisexpansion is constructed at order $1/m_Q^2$. A minimal set of universal formfactors is defined in terms of matrix elements of higher dimension operators inthe effective theory. The zero recoil normalization conditions following fromvector current conservation are derived. Several phenomenological applicationsof the general results are discussed in detail. It is argued that at zerorecoil the semileptonic decay rates for $B\to D\,\ell\,\nu$ and $B\toD^*\ell\,\nu$ receive only small second order corrections, which are unlikelyto exceed the level of a few percent. This supports the usefulness of the heavyquark expansion for a reliable determination of $V_{cb}$.Comment: (34 pages, REVTEX, two postscript figures available upon request),  SLAC-PUB-589

Second-order power corrections in the heavy-quark effective theory. I. Formalism and meson form factors