The ac-conductivity along the CuO2-layers of epitaxial films and single crystals of thicknesses 0.2µm≤ Lz ≤130µm reveals clear signatures for 2D-ordering. In particular, at Tc the screening length assumes the universal value LzΛT c /2νs predicted by the Kosterlitz-Thouless theory, which indicates that binding of long vortex strings nucleates long-range superconductivity in the present samples containing up to 10 5 CuO2-layers. Several details of the order-parameter dynamics remain unexplained.PACS numbers: 74.40.+k, 74.25.Fy, 74.72.Hs The layered structure of the high-T c oxide superconductors (HTSC) promotes the formation of topological exitations which may reduce T c to temperatures significantly below the mean-field value T c0 , where a finite Cooper-pair density n In order to provide a deeper insight into the ordering process in bulk (N ≫ 1) samples of the strongly layered HTSC Bi 2 Sr 2 CaCu 2 O 8 , where γ > ∼ 100, we present here a first study of the linear ac-conductivity σ(ω) in the highly conducting and fluctuating regime below T c0 . By scaling analyses, we determine static screening length λ 2 ± associated with superconducting and normal fluctuations above and below T c , respectively. For all temperatures above T c , λ 2 + provides quantitative evidence for 2D-ordering in the single crystals and the epitaxial film under study of thicknesses L z between 0.2µm and 130µm, and the dynamical shape of σ(ω) is described assuming 2D-fluctuations of the order parameter Ψ. At T c , the effective penetration depth 2λ 2 (T c )/L z agrees with the universal length associated with the KT transition. The high, universal value of the phase angle at T c , σ ′′ /σ ′ = 13.5 (1) 5 CuO 2 -planes, signatures of 3D-ordering appear only at temperatures below T c .Our inductive method for determining high ac conductivities from the measured linear magnetic susceptibility χ(ω) = χ ′ + iχ ′′ has been outlined before for bulk [14] and thin film [12] samples. Exact numerical relations between χ(ω) and σ(ω) = σ ′ + iσ ′′ were derived by E.H. Brandt for disks of arbitrary thickness [15], and using a complex inversion scheme, we evaluated σ(ω). We examine here a 0.2µm thick film epitaxially grown for SQUID fabrication [16] and crystalline discs of thicknesses between 13µm and 130µm, which were cleaved from the same crystal grown by L. Winkeler [17]. One of the great advantages of investigations of σ(ω) lies in the possibility of a precise determination of the onset for long-range superconductivity at the temperature where the frequency variation of the phase angle, d(σ ′′ /σ ′ )/dω, changes its sign [18].The first of such results for Bi 2 Sr 2 CaCu 2 O 8 are depicted in Fig.1 showing well defined intersections of the phase, i.e. d(σ ′′ /σ ′ )/dω = 0. Several novel features are seen. Despite the rather different T c 's of crystal and film, both attain there the same value of the phase angle, ϕ c ≡ arctan(σ ′′ /σ ′ ) Tc = 85.9 0 (8), in zero magnetic field. Since we observed the same value also on many other Bi 2 Sr 2 CaCu 2 O 8 ...