In an ultrasonic experiment, we have investigated the temperature profile of the velocity of longitudinal elastic waves propagating along a direction perpendicular to the layers in the organic superconductors κ-(BEDT-TTF)2X, X = Cu(SCN)2 and Cu[N(CN)2]Br. Although a small decrease of the velocity is observed at the superconducting transition, the most anomalous behavior is obtained in the normal metallic state where an important softening is identified around 40-50 K. In order to characterize the origin of this anomaly, we have studied its behavior under the application of hydrostatic pressure. The observed behavior is found to mimic those of the transport and magnetic properties of these materials which have been attributed to the magnetic fluctuations. Following the example of one-dimensional insulating systems where coupling between longitudinal acoustic waves and magnetic fluctuations is known to occur, our results suggest that the pseudo-gap regime of these two-dimensional organic superconductors is dominated by a similar mechanism.74.70. Kn, 74.25.Ld, 74.40.+k, 74.62.Fj Organic compounds of the κ-(BEDT-TTF) 2 X family are highly anisotropic, layered, extreme type II superconductors which show the highest superconducting transition temperatures known to date. 1 They are continuing to attrack considerable attention because of their similarity to the high T c cuprates and the possibility that they also have a non-conventional pairing state. 2 In these materials the superconducting phase is in close proximity to an antiferromagnetic (AF) phase. Indeed, at ambient pressure, the compounds with X = Cu[N(CN) 2 ]Br and Cu(SCN) 2 are showing superconducting ground states around 10 K, while an insulating one with antiferromagnetic ordering is obtained below 25 K for X = Cu[N(CN) 2 ]Cl. [3][4][5] However, the latter compound shows also a superconducting ground state around 12 K under a small hydrostatic pressure of 300 bar. 6 In view of the strong dimerization of the BEDT-TTF molecules, this pressure induced metal-insulator transition results from the competition between the repulsive Coulomb energy (U) and the bandwidth (W) in the effectively halffilled electronic band structure (Mott transition). 7 In the Cu[N(CN) 2 ]Br and Cu(SCN) 2 salts, the proximity of the AF magnetic phase can be infered from the transport and magnetic properties of the normal state. In NMR experiments the maximum of (T 1 T) −1 around 50 K and the rapid decrease of the Knight shift below 50 K were attributed to both AF magnetic fluctuations and to a pseudo-gap. 8,9 At the same temperature, the intra-and inter-layer resistivity data suggest a change of regime (peak in dR/dT) around the same temperature. 10 All these features observed on the magnetic and transport properties are highly sensitive to pressure and they completely disappear above 2 kbar. 9,10 Ultrasonic techniques can be used to study quasiparticle and magnetic excitations effects on the elastic properties of superconductors and attenuation measurements are probably the key exper...