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Résumé : We study some aspects of the infinite-momentum limit ${p}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ of amplitudes $M$ satisfying the requirements of Regge asymptotic behavior in the energy $s={(p\ensuremath{-}q)}^{2}={p}^{2}+{q}^{2}\ensuremath{-}2\ensuremath{\nu}$ (for the absorptive part) and Bjorken asymptotic behavior in the mass ${q}^{2}$ (we do not make essential use of space-space or time-derivative commutators). We also study how to incorporate the restrictions due to partial current conservation. These requirements shed much light on the nature of the ${p}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit and on the validity of its consequences. Thus, we may discuss the structure of current-algebraic sum rules, including possible infinite-mass contributions, in a purely analytical way and produce a sharper derivation of the Fubini-Dashen-Gell-Mann sum rule. To obtain a more complete understanding of the limit, we assume simple forms for the asymptotic behavior of $M$ in any direction in the $s\ensuremath{-}{q}^{2}$ plane. These model functions, which may be useful in phenomenological descriptions of asymptotic regions, smoothly interpolate between the Regge and Bjorken limits. They constitute an economical summary of the assumptions of current algebra, partial current conservation, Regge asymptotics, and validity of the infinite-momentum procedure. Although their forms are only partially justified, they lead to testable predictions concerning the saturation properties of asymptotic sum rules, the existence of new fixed-mass sum rules, and behavior in the limit $\ensuremath{\nu}\ensuremath{\rightarrow}\ensuremath{\infty}$, ${q}^{2}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, $\frac{\ensuremath{\nu}}{{q}^{2}}$ fixed. In terms of this model, exact criteria for the validity of interchanging the infinite-momentum limit with energy integrations can be obtained, and previous results, deduced from properties of free-field theories, can be extended to the interaction case.