Aims. Deflagration models poorly explain the observed diversity of SNIa. Current multidimensional simulations of SNIa predict a significant amount of, so far unobserved, carbon and oxygen moving at low velocities. It has been proposed that these drawbacks can be resolved if there is a sudden jump to a detonation (delayed detonation), but these kinds of models have been explored mainly in one dimension. Here we present new three-dimensional delayed detonation models in which the deflagraton-to-detonation transition (DDT) takes place in conditions like those favored by one-dimensional models. Methods. We have used a smoothed-particle-hydrodynamics code adapted to follow all the dynamical phases of the explosion, with algorithms devised to handle subsonic as well as supersonic combustion fronts. The starting point was a centrally ignited C-O white dwarf of 1.38 M . When the average density on the flame surface reached ∼2−3 × 10 7 g cm −3 a detonation was launched. Results. The detonation wave processed more than 0.3 M of carbon and oxygen, emptying the central regions of the ejecta of unburned fuel and raising its kinetic energy close to the fiducial 10 51 erg expected from a healthy type Ia supernova. The final amount of 56 Ni synthesized also was in the correct range. However, the mass of carbon and oxygen ejected is still too high. Conclusions. The three-dimensional delayed detonation models explored here show an improvement over pure deflagration models, but they still fail to coincide with basic observational constraints. However, there are many aspects of the model that are still poorly known (geometry of flame ignition, mechanism of DDT, properties of detonation waves traversing a mixture of fuel and ashes). Therefore, it will be worth pursuing its exploration to see if a good SNIa model based on the three-dimensional delayed detonation scenario can be obtained.