We have discovered new features of the current-phase relation, I(phi), in s
uperfluid He-3 weak links. Firstly, we find that at any given temperature t
here are two distinct I(phi) functions that characterize the weak link. Sec
ondly, both functions continuously develop an unusual form that ultimately
leads to the previously reported pi state. The observed form of I(phi) has
recently been predicted for unconventional quantum fluids such as He-3, hig
h-T-c superconductors, and Bose-Einstein condensates. The two distinct stat
es are likely to originate from the textural degree of freedom in superflui
d He-3.