We report an extensive study on the temperature (T) dependence of the
upper critical field H-c2 on Ba1-xKxBiO3 single crystals. The H-c2(T)
curve shows a reproducible upward curvature at similar to 22 K. This c
an be hue to the presence of two superconducting phases, one with T-c
similar to 30 K and low H-c2 ([dH(c2)/dT](Tc) similar to 0.5 T/K) and
another one with T-c similar to 25 K and higher H-c2 ([dH(c2)/dT](Tc)
similar to 1.1 T/K). However, we find that H-c2 may rise up to 32 T at
1.8 K. It turns out that the reduced critical field h(c2) = H-c2/[T-c
(dH(c2)/dT)(Tc)] is greater than or equal to 1 at low temperatures for
both the 30- and 25-K phases, i.e., much higher than what is expected
for a conventional superconductor. We compare the low-temperature h(c
2) data with calculations recently performed by Marsiglio and Carbotte
in the framework of an extended Werthamer-Helfand-Hohenberg theory.