A scan of the superconductor-nonsuperconductor transformation in single crystals of YBa2Cu3O6+x (x approximate to 0.37) is done in two alternative ways, namely, by applying a magnetic field and by reducing the hole concentration through oxygen rearrangement. The in-plane normal-state resistivity rho(ab) Obtained in the two cases is quite similar; its temperature dependence can be fitted by a logarithmic law in a temperature range of almost two decades. However, an alternative representation of the temperature dependence of sigma(ab) = 1/rho(ab) by a power law, typical for a 3D material near a metal-insulator transition, is also plausible. The vertical conductivity sigma(c) = 1/p(c) followed a power law, and neither sigma(c)(T), nor rho(c)(T) could be fitted by log T. It follows from the rho(c) measurements that the transformation at T = 0 is split into two transitions: superconductor- normal-metal and normal-metal-insulator. In our samples, they are separated in oxygen content by Delta x approximate to 0.025. (C) 1997 American Institute of Physics.