  We demonstrate experimentally the existence of Josephson junctions having a
doubly degenerate ground state with an average Josephson phase \psi=\pm{\phi}.
The value of {\phi} can be chosen by design in the interval 0<{\phi}<\pi. The
junctions used in our experiments are fabricated as 0-{\pi} Josephson junctions
of moderate normalized length with asymmetric 0 and {\pi} regions. We show that
(a) these {\phi} Josephson junctions have two critical currents, corresponding
to the escape of the phase {\psi} from -{\phi} and +{\phi} states; (b) the
phase {\psi} can be set to a particular state by tuning an external magnetic
field or (c) by using a proper bias current sweep sequence. The experimental
observations are in agreement with previous theoretical predictions.
