Dijet production in deep inelastic ep scattering is investigated in the region of low values of the Bjorken-variable x (10(-4) <x <10(-2)) and low photon virtualities Q(2) (5 <Q(2) <100 GeV2). The measured dijet cross sections are compared with perturbative QCD calculations in next-to-leading order. For most dijet variables studied, these calculations can provide a reasonable description of the data over the full phase space region covered, including the region of very low x. However, large discrepancies at low x and low Q(2) are observed for events with small separation in azimuth between the two highest transverse momentum jets. This region of phase space is described better by predictions based on the CCFM evolution equation, which incorporates k(t) factorized unintegrated parton distributions. A reasonable description can be also obtained using the Color Dipole Model or models incorporating virtual photon structure.