We explore the question of whether dust envelopes can survive around t
he secondary components of the B stars BM Ori and V1016 Ori. The assum
ption that such envelopes exist is shown to be unavoidable. Two altern
ative compositions of these envelopes are considered: graphite and alp
ha-cristobalite (alpha-SiO2, the refractory modification of quartz). F
or the graphite envelope around the secondary of BM Ori, we have faile
d to unambigously solve the question of its survival. The mean grain t
emperature is below the graphite sublimation temperature. In the case
of intense mixing, the envelope does not evaporate. If, however, the e
nvelope is static (the case of corotation), then the dust temperature
turns out to be lower than the sublimation temperature in 67% of the e
nvelope and high in its remaining part (33%). The envelope then evapor
ates. Model calculations show that 98% of the envelope does not evapor
ate in: the case of grains coagulation, and, accordingly, it survives.
Since the temperature of the entire quartz envelope is below the quar
tz melting temperature, such an envelope can exist. An envelope made u
p of graphite dust grains definitely cannot exist around the secondary
of V1016 Ori-such dust evaporates. However, an envelope composed of q
uartz grains can exist. In this case, quartz remains in a solid phase.
We propose an observational check on the derived temperature distribu
tion in the envelopes. To this end, we compare the temperatures and ra
dii of the envelopes that we determined by analyzing the stars' contin
uum in the bands from to M with those estimated from the dust-envelope
models. The JHKL observations of deep minima in BM Ori also lend supp
ort to the dust-envelope model. In the Appendix, we solve the light cu
rve of V1016 Ori by assuming that the primary star is eclipsed both by
the secondary and by the dust envelope. This solution is in satisfact
ory agreement with the observations.