Classical strings coupled to a metric, a dilaton and an axion, as
conceived by superstring theory, suffer from ultraviolet divergences
due to self-interactions. Consequently, as in the case of
radiating charged particles, the corresponding effective string dynamics
cannot be derived from an action principle. We propose a
fundamental principle to build this dynamics, based on local energymomentum
conservation in terms of a well-defined
distribution-valued energy-momentum tensor. Its continuity
equation implies a finite equation of motion for self-interacting
strings. The construction is carried out explicitly for strings in
uniform motion in arbitrary space\u2013time dimensions, where we
establish cancelations of ultraviolet divergences which parallel
superstring non-renormalization theorems. The uniqueness properties
of the resulting dynamics are analyzed
