  We point out that there exist two different formulations of the Heavy Quark
Effective Theory (HQET). One formulation of HQET was mostly developed at
Harvard and involves the use of the equation of motion to eliminate the small
components of the heavy quark field. The second formulation, developed in
Mainz, involves a series of Foldy-Wouthuysen-type field transformations which
diagonalizes the heavy quark Lagrangian. Starting at O($1/m_Q^2$) the two
formulations are different in that their effective Lagrangians, their effective
currents, and their fields differ. However, when these three differences are
properly taken into account, the two alternative formulations lead to identical
S-matrix elements. This is demonstrated in an explicit example at O($1/m_Q^2$).
We point to an essential difficulty of the Harvard HQET in that the Harvard
effective fields are not properly normalized starting at order $O(1/m_Q^2)$.
