  Two supernovae detected in the Hubble Deep Field using the original December
1995 epoch and data from a shorter (63000 s in F814W) December 1997 visit with
HST are discussed. The supernovae (SNe) are both associated with distinct
galaxies at redshifts of 0.95 (spectroscopic) from Cohen etal. (1996) and 1.32
(photometric) from the work of Fernandez-Soto, Lanzetta, and Yahil (1998).
These redshifts are near, in the case of 0.95, and well beyond for 1.32 the
greatest distance reported previously for SNe. We show that our observations
are sensitive to SNe to z < 1.8 in either epoch for an event near peak
brightness. Detailed simulations are discussed that quantify the level at which
false events from our search phase would start to to arise, and the
completeness of our search as a function of both SN brightness and host galaxy
redshift. The number of Type Ia and Type II SNe expected as a function of
redshift in the two HDF epochs are discussed in relation to several published
predictions and our own detailed calculations. A mean detection frequency of
one SN per epoch for the small HDF area is consistent with expectations from
current theory.
