  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 can not be derived from an action
principle. We propose a fundamental principle to build this dynamics, based on
local energy-momentum 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-time
dimensions, where we establish cancelations of ultraviolet divergences which
parallel superstring non-renormalization theorems. The uniqueness properties of
the resulting dynamics are analyzed.
