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.

62 pages, 17 figures, ApJ 1999 in press