  We present a general method to match fully differential
next-to-next-to-leading (NNLO) calculations to parton shower programs. We
discuss in detail the perturbative accuracy criteria a complete NNLO+PS
matching has to satisfy. Our method is based on consistently improving a given
NNLO calculation with the leading-logarithmic (LL) resummation in a chosen jet
resolution variable. The resulting NNLO$+$LL calculation is cast in the form of
an event generator for physical events that can be directly interfaced with a
parton shower routine, and we give an explicit construction of the input "Monte
Carlo cross sections" satisfying all required criteria. We also show how other
proposed approaches naturally arise as special cases in our method.
