We propose a three stage algorithm to build all 3D-horizons simultaneously in volume seismic data. To improve reliability, this algorithm takes into consideration the relative positions of all horizons, and uses globally self consistent connectivity criteria which respect the temporal order of horizon creation. The first stage consists of the preliminary estimation of the local direction of each horizon at each point of the 3D-space. The second is smoothing the signal along the detected layer structure to reduce the level of noise in the signal. The basic processing is realized at the last stage of the algorithm. The processed 3D-seismic data are used for the simultaneous building of all 3D horizons. The output of the processing is a set of 3D-horizons represented by a series of triangulated surfaces.