The paper tries to sort out the specific signatures of the Near Earth Neutral Line (NENL) and the Current Disruption (CD) models. and looks for these signatures in Cluster data from two events. For both events transient magnetic si-natures are observed, together with fast ion flows. In the simplest form of NENL scenario, with a large-scale two-dimensional reconnection site, quasi-invariance along Y is expected. Thus the magnetic signatures in the S/C frame are interpreted as relative motions, along the X or Z direction, of a quasi-steady X-line, with respect to the S/C. In the simplest form of CD scenario an azimuthal modulation is expected. Hence the signatures in the S/C frame are interpreted as signatures of azimuthally (along Y) moving current system associated with low frequency fluctuations of J(y) and the corresponding field-aligned currents Event I covers a pseudo-breakup, developing only at high latitudes. First, a thin (H approximate to 2000Km approximate to 2 rho(i), with pi the ion gyroradius) Current Sheet (CS) is found to be quiet. A slightly thinner CS (H approximate to 1000-2000 km approximate to 1-2 rho(i)), crossed about 30 min later, is found to be active. with fast earthward ion flow bursts (300-600 km/s) and simultaneous large amplitude fluctuations (delta B/B similar to 1). In the quiet CS the current density J(y) is carried by ions. Conversely, in the active CS ions are moving eastward; the westward current is carried by electrons that move eastward, faster than ions. Similarly, the velocity of earthward flows (300-600 km/s), observed during the active period. maximizes near or at the CS center. During the active phase of Event I no signature of the crossing of an X-line is identified, but an X-line located beyond Cluster could account for the observed ion flows, provided that it is active for at least 20 min. Ion flow bursts can also be due to CD and to the corresponding dipolarizations which are associated with changes in the current density. Yet their durations are shorter than the duration of the active period. While the overall partial derivative Bz/partial derivative t is too weak to accelerate ions up to the observed velocities, short duration partial derivative B-z/partial derivative t can produce the azimuthal electric field requested to account for the observed ion flow bursts. The corresponding large amplitude perturbations are shown to move eastward. which suggests that the reduction in the tail current could be achieved via a series of eastward traveling partial dipolarisations/CD. The second event is much more active than the first one. The observed flapping of the CS corresponds to an azimuthally propagating wave. A reversal in the proton flow velocity, from 1000 to + 1000 km/s, is measured by CODIF. The overall flow reversal, the associated change in the sign of B-z and the relationship between B-x and B-y suggest that the spacecraft are moving with respect to an X-line and its associated Hall-structure. Yet, a simple tailward retreat of a large-scale X-line cannot account for all the observations, since several flow reversals are observed. These quasi-periodic flow reversals can also be associated with an azimuthal motion of the low frequency oscillations. Indeed, at the beginning of the interval B-y varies rapidly along the Y direction; the magnetic signature is three-dimensional and essentially corresponds to a structure of filamentary field-aligned current, moving eastward at similar to 200 km/s. The transverse size of the structure is similar to 1000 km. Similar structures are observed before and after. Thesefilamentary structures are consistent with an eastward propagation of an azimuthal modulation associated with a current system J(y), J(x). During Event 1, signatures of filamentary field-aligned current structures are also observed, in association with modulations of J(y). Hence, for both events the structure of the magnetic fields and currents is three-dimensional.