A new subclass of weakly ionized BAL-quasars, introduced by Becker ed al. (
1997) and represented by three quasars, 1556+3517, 0840+3633, and 0059-2735
, is considered. Their optical spectra are distinguished by extremely stron
g absorption both in the lines and in the continuum, as well as by the abse
nce of emission features. These peculiarities of the spectra can be explain
ed by the presence of molecules, which are responsible for strong absorptio
n lines, in the outer layers of these quasars. In particular, it is propose
d to identify again the line lambda = 2063 Angstrom (assigned to CrII) as t
he line belonging to the Cameron band a(3)Pi(i) <-- X(1)Sigma(+) of the CO
molecule. The expected optical depth in the rotational transition of the mo
lecule is estimated. It is proposed to carry out radio observations of thes
e quasars to test the molecular hypothesis.