Results are presented of integrations of a representative sample of th
ousands of test bodies in the Kuiper belt for times up to the age of t
he solar system. Using this survey, the main regions of dynamical stab
ility (and instability) are mapped out as a function of the particles'
semi-major axes, eccentricities, and inclinations. Much of the dynami
cal structure is shown to be correlated with mean motion and secular r
esonances. Weak dynamical instabilities are confirmed to be capable of
producing an influx of Neptune-approaching bodies even on Gyr time sc
ales. The integrations are also compared with current observations of
bodies in this region. Implications for the early evolution of the Kui
per belt, its current structure, and the origins of short-period comet
s are discussed. (C) 1995 American Astronomical Society.