  In a Wilsonian renormalization group (RG) analysis, redundant operators,
which may be eliminated by using field redefinitions, emerge naturally. It is
therefore important to include them. We consider a nonrelativisitic effective
theory (the so-called ``pionless'' Nuclear Effective Field Theory) as a
concrete example and show that the off-shell amplitudes cannot be renormalized
if the redundant operators are not included. The relation between the theories
with and without such redundant operators is established in the low-energy
expansion. We perform a Wilsonian RG analysis for the \textit{off-shell}
scattering amplitude in the theory with the redundant operator.
