Micromagnetic structures are computed for pairs of 180° domain walls in thin films, driven together by applied magnetic fields. It is shown that the field required to annihilate the walls depends strongly on their relative symmetry. There are six possible symmetries for pairs of walls, two of which show no resistance to annihilation. For the other four symmetries, the applied field needed to annihilate the walls varies by large amounts according to the symmetry. The resistance to annihilation decreases with increasing film thickness. Experimental studies of interactions of domain‐wall pairs, in which examples of both low and fairly high resistance to annihilation have been observed, provide qualitative support for these results. It is concluded that wall interactions can contribute significantly to the coercivity of soft magnetic films.