  We develop threshold resummation for single-particle inclusive cross sections
in hadron-hadron collisions to the level of next-to-next-to-leading logarithm,
up to full matching with two-loop hard functions. We define and calculate all
one-loop soft functions for all partonic channels. This enables us to separate
the hard and soft functions at one loop. Along with these results, the one-loop
finite parts of jet functions are used to check that the full soft, collinear
and virtual corrections are reproduced to one loop for all partonic reactions.
We exhibit these NLO results explicitly. NLO expansions of the resummed cross
section match the exact NLO results extremely well numerically, and two loop
expansions result in substantial corrections over many kinematic
configurations. Explicit results are given in Mellin moment space, and a number
of options for generating resummed cross sections are discussed.
