We report muon spin rotation studies of the magnetic field distribution n(B) in the vortex state of the high-temperature superconductor Bi2 Sr2 CaCu2 O8+δ. From our data on three sets of overdoped, nearly optimized and underdoped smgle crystals we obtain evidence for a two-stage melting process of the vortex matter under equilibrium. conditions. In the irreversible regime well below the irreversibility line we observe a transition in the vortex state which we associate with an intra-planar melting transition. The resulting flux-lme liquid phase persists over a sizeable temperature interval before the inter-planar decoupling of the mdividual vortex lines takes place in a second step at the irreversibility lme, resultmg in a pancake liquid phase.PACS numbers: 74.60. Ge, 74.25.Dw, 74.72.Hs, 76.75.+i The vortex matter in cuprate high-T c superconductors exhibits a complex (H, T)-phase diagram as a function of magnetic field, temperature and doping [1]. The short superconducting (SC) coherence length, the high transition temperatures and the strongly anisotropic layered structure favor thermal fluctuations which dominate the vortex state well below the upper critical field H c2(T). In contrast to conventional type-II superconductors, a melting transition of the flux-line lattice (FLL) was proposed [2] and confirmed experimentally [3]. Nevertheless, the details of this melting transition are not yet fully understood.(245)