We present approximations to tree-level multiparton scattering amplitu
des which are appropriate when two partons are unresolved. These appro
ximations are required for the analytic isolation of infrared singular
ities of n + 2 parton scattering processes contributing to the next-to
-next-to-leading order corrections to n jet cross sections. In each ca
se the colour ordered matrix elements factorise and yield a function c
ontaining the singular factors multiplying the n-parton amplitudes. Wh
en the unresolved particles are colour unconnected, the approximations
are simple products of the familiar eikonal and Altarelli-Parisi spli
tting functions used to describe single unresolved emission. However,
when the unresolved particles are colour connected the factorisation i
s more complicated and we introduce new and general functions to descr
ibe the triple collinear and soft/collinear limits in addition to the
known double soft gluon limits of Berends and Giele. As expected the t
riple collinear splitting functions obey an N = 1 SUSY identity. To il
lustrate the use of these double unresolved approximations, we have ex
amined the singular limits of the tree-level matrix elements for e(+)e
(-) --> 5 partons when only three partons are resolved. When integrate
d over the unresolved regions of phase space, these expressions will b
e of use in evaluating the O(alpha(s)(3)) corrections to the three-jet
rate in electron-positron annihilation. (C) 1998 Elsevier Science B.V
.