We present magnetic-torque measurements of the organic superconductor k-(BEDT-TTF)2Cu(NCS)2 for in-plane magnetic fields up to 32 T. In this layered two-dimensional compound the superconductivity can persist even in fields above the Pauli limit of about 21 T. There, a pronounced upturn of the upper-critical-field line occurs and the superconducting phase-transition line splits and forms an additional high magnetic field phase. k-(BEDT-TTF)2Cu(NCS)2 is a spin-singlet superconductor, therefore,

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... ch a superconducting high-field phase beyond the Pauli limit can originate only from Cooper pairing with finite center-of-mass momentum. The measurements are discussed in connection with a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in accordance with earlier specific-heat observations. The torque experiments allow us to investigate the high magnetic-field phase diagram and the FFLO state of k-(BEDT-TTF)2Cu(NCS)2 in great detail.