Previous approaches to the photo- and electro-production of strangeness off the proton, based upon effective hadronic Lagrangians, are extended here to incorporate the so called off-shell effects inherent to the fermions with spin >= 3/2. A formalism for intermediate-state, spin 3/2, nucleonic and hyperonic resonances is presented and applied to the processes $gamma + p ---> K^{+} + Lambda$, for $E_{gamma}^{lab}$ <= 2.5 GeV, $e + p ---> e + K^+ + Lambda$, as well as the branching ratio for the crossed channel reaction $K^- + p ---> gamma + Lambda$, with stopped kaons. The sensitivity, from moderate to significant, of various observables to such effects are discussed.
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