  Cross sections for inclusive dijet production in diffractive deep-inelastic
scattering are calculated for the first time in next-to-next-to-leading order
(NNLO) accuracy. These cross sections are compared to several HERA measurements
published by the H1 and ZEUS collaborations. We computed the total cross
sections, 49 single-differential and five double-differential distributions for
six HERA measurements. The NNLO corrections are found to be large and positive.
The normalization of the resulting predictions typically exceeds the data,
while the kinematical shape of the data is described better at NNLO than at
next-to-leading order (NLO). Our results use the currently available NLO
diffractive parton distributions, and the discrepancy in normalization
highlights the need for a consistent determination of these distributions at
NNLO accuracy.
