In organic conductors the overlap integral between layers is small In-plane momentum scattering is rapid and transport perpendicular to the layers is expected to be blocked We present a high frequency conduction electron spin resonance (CESR) study in the layered organic metals kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]X, X = Cl Br which verifies that the inter-layer spin hopping is effectively blocked The method relies on resolving the CESR lines of adjacent layers in which the orientation of the g-factor tensors differs We find that at ambient pressure and in the metallic phase the electron spin diffusion is two dimensional in both the X = Cl and Br compounds i e electrons diffuse longer than the spin lifetime within a single molecular layer without inter-layer hopping Application of pressure at 250 K Increases rapidly the inter-layer hopping rate of spins (C) 2009 Elsevier B V All rights reserved