We present a time-averaged spectral analysis (0.1-100 MeV) of two intense g
amma-ray bursts detected by the PHEBUS experiment. The vf(v) spectra of the
se two events are observed to peak between 1 and 2 MeV. For the least inten
se of the two bursts, a single maximum in vf(v) is seen. For the other, the
re is a suggestion of two peaks, with similar strengths, at similar to 1 an
d similar to 2 MeV. The most commonly used photon models, with four or five
parameters, provide inadequate frits to the latter spectrum. We have teste
d two seven-parameter models that satisfactorily fit the observations by th
e two brightest detectors of the stronger event. Both of them are built fro
m and compared with the standard four-parameter gamma-ray burst (GRB) funct
ion. The first model assumes an additional emission described by a Gaussian
expression. The second one supposes a further spectral break at higher ene
rgy. For the two models, we find an extra emission around 2 MeV relative to
the standard GRB model. In addition, the second seven-parameter model supp
orts a sudden change in the photon spectral index from about -2 to -3.6 ove
r a restricted energy range near 2.4 MeV. The probability of rejecting, as
due to chance, these two models relative to the standard four-parameter exp
ression does not exceed 6.8 x 10(-8). Although its origin is unclear, the 2
MeV emission excess may provide important constraints on the physical cond
itions and radiation mechanisms at the emission site of gamma-ray bursts.