Lee and Stroud have predicted that the critical current I(c)(B) in a c
omposite superconducting material should displav a constant value in m
oderately high magnetic fields, giving rise to a 'plateau region'. Cri
tical current measurements on granular metallic Al-Ge films, located c
onsiderably above the metal-insulator transition (MIT), display well d
efined plateaus, and these measurements confirm most of the Lee-Stroud
predictions. In contrast, films located just above the MIT exhibit co
ntinuously decreasing critical currents with increasing magnetic field
s. These results are explained using a tunnelling junction model propo
sed by Peterson and Ekin and extended by Papa and Altshuler. From the
fitting results, a simple picture, involving both models, emerges, whi
ch explains the behaviour of I(c) versus magnetic field in pressed pow
dered YBCO samples and in Ag-sheathed Bi-based HTC wires, as well as i
n the Al-Ge films.