Low-mass helium star models that reproduce the first 100 days of the l
ight curve of the Type Ic SN 1987M are used in model atmosphere calcul
ations. The resulting spectra are compared to observations from 60 to
140 days post-maximum. The small column depth to Co-56 decay photons l
eads to strong optical helium lines at 60 days after maximum which fad
e into the continuum for times t greater than or similar to 200 days w
hile the He I 10830 angstrom line remains a strong P-Cygni feature at
all times examined. The lack of observed optical helium lines suggests
SN 1987M has a low helium abundance with a total helium mass fraction
not much in excess of approximately 7%. This suggests a significantly
different evolutionary path from the helium-rich Type Ib SN 1984L. Th
e effects on the theoretical spectrum of mixing the ejecta and/or arti
ficially converting the helium to oxygen are also explored. In spite o
f very large departure coefficients, the predicted optical helium line
s at late times are not strong enough to be identified in the current
Type Ib or Type Ic data base. This provides an explanation for the sim
ilarity between optical spectra of these supernova subtypes at times e
xceeding about 200 days even if Type Ib contain substantial amounts of
helium and Type Ic do not. The spectroscopic implications for Type Ic
progenitor evolution, including the possible presence of a small amou
nt of hydrogen in the ejecta, is discussed.