We present high precision measurements of the penetration depth of single crystals of κ−(ET)2Cu[N(CN)2]Br and κ−(ET)2Cu(NCS)2 at temperatures down to 0.4 K. We find that, at low temperatures, the in-plane penetration depth (λ ) varies as a fractional power law, λ ∼ T 3 2 . Whilst this may be taken as evidence for novel pair excitation processes, we show that the data are also consistent with a quasilinear variation of the superfluid density, as is expected for a d-wave superconductor with impurities or a small residual gap. Our data for the interplane penetration depth show similar features and give a direct measurement of the absolute value, λ ⊥ (0) = 100 ± 20 µm.PACS numbers: 74.70. Kn, 74.25.Nf Compounds of the family κ−(ET) 2 X have the highest transition temperatures of all organic superconductors known to date [1]. They have recently attracted considerable attention because of their similarity to the high T c cuprates and the possibility that they may also have a non-conventional paring state [2]. The two materials studied here, κ−(ET) 2 Cu[N(CN) 2 ]Br (T c ∼ 11.6 K) and κ−(ET) 2 Cu(NCS) 2 (T c ∼ 9.6 K), are highly anisotropic, layered, extreme type II superconductors. As in the cuprates, the superconducting phase in these materials is in close proximity to an antiferromagnetic phase. Both antiferromagnetic spin fluctuations and a pseudogap have been detected in NMR measurements in the normal state [3]. Neither the underlying pairing mechanism nor the symmetry of the order parameter has been conclusively established. Although NMR [4,5], specific heat [6] and thermal conductivity [7] measurements all suggest a non-conventional pairing state, results of penetration depth measurements have been inconsistent, with evidence for both conventional [8,9] and non-conventional [10][11][12] behavior. However, none of these penetration depth measurements have been performed over a temperature range (T /T c ) and a precision, comparable to those in the cuprates [13]. In this Letter, we present measurements of both the in-plane λ , and the interplane, λ ⊥ , penetration depths in κ−(ET) 2 Cu[N(CN) 2 ]Br and κ−(ET) 2 Cu(NCS) 2 at temperatures down to 0.4 K.Our measurements were performed on single crystals of κ−(ET) 2 Cu[N(CN) 2 ]Br and κ−(ET) 2 Cu(NCS) 2 which were grown at Argonne National Laboratory. Details of the growth procedures have been given elsewhere [14]. Penetration depth measurements were performed using a 13 MHz tunnel diode oscillator [15] mounted on a 3 He refrigerator. The low noise level [ ∆F F0 ≃ 10 −9 ], and low drift of the oscillator allows us to obtain high resolution data with a very small temperature spacing interval. The samples were attached, with a small amount of vacuum grease, to a sapphire rod which fitted inside the copper sense coil. The sense coil was calibrated using spheres of Aluminum. The sample temperature was measured with a calibrated Cernox thermometer attached to the other end of the sapphire rod. The samples were cooled slowly (0.1-1.0 K/min) to avoid introducing disorder [1...