Relations between the existence of ODLRO in the reduced density matrixρ
n
(for alln≧1) and that of superconducting currents in a hollow cylinder are discussed. Some concrete behaviours ofρ
n
, including the power law decaying behaviour, in the coordinate space representation are considered and the corresponding effective superconducting particle densities are given. Some restraint conditions caused by the existence of the ODLRO (including quasi-ODLRO) have been found and discussions on the minimum unit of flux quantization are also included.