  A mathematical model in terms of partial differential equations (PDE) for the
calculation of double freeform surfaces for irradiance and phase control with
predefined input and output wavefronts is presented. It extends the results of
B\"osel and Gross [J. Opt. Soc. Am. A 34, 1490 (2017)] for the illumination
design of single freeform surfaces for zero-\'etendue light sources to double
freeform lenses and mirrors. The PDE model thereby overcomes the restriction to
paraxiality or the requirement of at least one planar wavefront of the current
design models in the literature. In contrast with the single freeform
illumination design, the PDE system does not reduce to a Monge-Amp\`ere type
equation for the unknown freeform surfaces, if nonplanar input and output
wavefronts are assumed. Additionally, a numerical solving strategy for the PDE
model is presented. To show its efficiency, the algorithm is applied to the
design of a double freeform mirror system and double freeform lens system.
