We report on dc-magnetization measurements on high-quality single crystals of the organic superconductors κ-(BEDT-TTF)2 Cu(NCS)2 and κ-(BEDT-TTF)2Cu[N(CN)2]Br for fields parallel and perpendicular to the conducting planes. For H perpendicular to the planes, we find clear indications for strong superconducting fluctuations, i.e., a pronounced rounding of the transition with increasing field and field-induced diamagnetism above Tc. Careful experiments near Tc reveal the existence of a field-independent magnetization at M*(T*,H) for H≤10 kOe. The anisotropy of superconducting parameters such as the upper critical field and coherence length, along with a scaling form of the high-field magnetization data demonstrate the highly anisotropic character for the present superconductors. Over an extended range in the H-T plane the mixed-state properties are governed by an entirely reversible vortex motion. The lower boundary of this range, the so-called irreversibility line, is found to be anisotropic and, for H perpendicular to the planes, to follow an exponential T dependence. Cooling below the irreversibility line is accompanied by the occurrence of magnetic relaxation effects, indicating a metastable vortex state.