Muon-spin rotation (mu SR) measurements have been used to study the superconducting vortex properties of the organic superconductors kappa-(BEDT-TTTF)(2) Cu(SCN)(2), alpha-(BEDT-TTF)(2) NH4Hg(SCN)(4) and beta-(BEDT-TTF)(2)IBr2. These materials all have highly anisotropic structures consisting of metallic layers of BEDT-TTF molecules alternating with less well conducting anion layers. Varying the anion gives rise to a change in the anisotropy of the superconductivity and also to changes in the superconducting transition temperature. We have used both transverse and longitudinal magnetic fields to study the three-dimensional flux line lattice that is present at low temperatures and fields and to study also the loss of flux lattice order that occurs on increasing the temperature and field. (C) 2000 Elsevier Science B.V. All rights reserved.