Using a micro-Hall probe, measurements of field of first flux penetrat
ion H(p) and the critical current density J(c) have been made near T(c
) of superconducting Bi2Sr2CaCu2O8. In the temperature region just bel
ow T(c)=86.0 K; T(s) < T < T(c), it was found that H(p) and J(c) are s
trongly suppressed, leaving a reversible diamagnetic susceptibility. N
o similar effect is observed in YBa2Cu3O7-y which suggests that the hi
ghly two-dimensional character of Bi2Sr2CaCu2O8 is responsible for its
particular behavior. The results are compared with recent theoretical
predictions.