The superconducting transitions of the highly anisotropic metals TaSe3 and NbSe3 were investigated using SQUID magnetometers. The observed diamagnetic susceptibility showed similar unusual field and temperature dependences for both materials. In particular, the susceptibility of the samples in low fields increased greatly at temperatures far below the transition temperature of the material (as indicated by the onset of temperature dependent diamagnetism and the upper limit of flux trapping). The measurements suggest the presence of a second transition at low tempeatures where small superconducting regions of the sample become coupled throughout larger volumes.