The tautomerism of furoxan (1,2,5-oxadiazole-2-oxide) has been investigated by different computational methods comprising modem density functionals as well as single-reference and multi-reference ab initio methods. The ring-opening process to 1,2-dinitrosoethylene is the most critical step of the reaction and cannot be treated reliably by low-level computations. The existence of cis-cis-trans-1,2-dinitrosoethylene as a stable intermediate is advocated by perturbational methods, but high-level coupled-cluster calculations identify this as an artifact. In contrast to the analogous reaction in benzofuroxans, cis-cis-cis-1,2-dinitrosoethylene was found to be a transition state rather than a local minimum. Model potentials were used to explain the occurrence and the disappearing of transition states and local minima relative to the reaction of benzofuroxan. Low-lying triplet states that can be accessed due to spin-orbit coupling were investigated as taking part in alternative routes to a proposed singlet pathway. Barriers for rotations of the nitroso groups on the S-0 and T-1 surfaces are reported.