We derive the angular correlation functions between an arbitary number
of partons inside a quark or gluon jet emerging from a high energy ha
rd collision. As an application results for the correlation in the rel
ative angle between two partons as well as the multiplicity moments of
any order for partons in a sidewise angular region are calculated. At
asymptotic energies the distributions of rescaled angular variables a
pproach a scaling limit of a new type with two redundant quantities. A
ll observables reveal the power behaviour characteristic to the fully
developed selfsimilar cascade in appropriate regions of phase space. W
e present analytical results from the double logarithmic approximation
as well as Monte Carlo results.