We investigate iterative trellis decoding techniques for DAB, with the objective of gaining from processing 2D-blocks in an OFDM scheme, that is, blocks based on the time and frequency dimension, and from trellis decomposition. Trellis-decomposition methods allow us to estimate the unknown channel phase since this phase relates to the sub-trellises. We will determine a-posteriori sub-trellis probabilities, and use these probabilities for weighting the a-posteriori symbol probabilities resulting from all the sub-trellises. Alternatively we can determine a dominant sub-trellis and use the a-posteriori symbol probabilities corresponding to this dominant sub-trellis. This dominant sub-trellis approach results in a significant complexity reduction. We will investigate both iterative and non-iterative methods. The advantage of non-iterative methods is that their forwardbackward procedures are extremely simple; however, also their gain of 0.7dB, relative to two-symbol differential detection (2SDD) at a BER of 10-4, is modest. Iterative procedures lead to the significantly larger gain of 3.7dB at a BER of 10-4 for five iterations, where a part of this gain comes from 2D processing. Simulations of our iterative approach applied to the TU-6 (COST207) channel show that we get an improvement of 2.4dB at a Doppler frequency of 10Hz.