A new approach to the study of the phase transitions in the organic superconductors kappa-(BEDT-TTF)2X has been used which involves the measurement of the cooling rate effects on the transport properties of these materials. In non-deuterated and deuterated kappa-(BEDT-TTF) 2Cu[N(CN)2]Br compounds, the sample resistivity turns out to increase significantly with increasing cooling rate (through 80 K) for temperature below 80 K. However, it is unaffected above this temperature. If directly quenched from various high temperatures to 77 K, the resistivity can undergo exponential relaxation processes with the same characteristic time constant about 500 second in the kappa-(BEDT-TTF)2Cu[N(CN) 2]Br compound. However, the relaxation amplitude increases monotonically with increase of quenching temperature up to 140 K, and becomes a constant above this temperature. The superconducting transitions in these compounds are also found to depend on the cooling through 80 K. A modified Ising model is used as an approximation to discuss the phase transitions and pressure effect. For the first time, a relatively accurate T-P phase diagram is constructed for kappa-(ET)2X compounds. The interlayer magnetoresistances of compounds of kappa-(ET)2Cu[N(CN)2]Br and beta \u27\u27-(ET)2SF5CH 2CF2SO3 display anomalous peak effects as functions of magnetic field in the mixed state. The experimental data can be well fitted by taking into account the parallel conduction channels of stacked Josephson junctions and normal vortex cores. The peak effect in kappa-(ET)2Cu[N(CN) 2]Br is found to increase with increase of cooling rate. However, their curves (of magnetoresistance versus field) associated with different cooling rates can be scaled to overlap each other
