We investigate the radiative dileptonic decays B-s(B-d) --> gamma l(+)
l(-) within the standard model. Using the constituent quark model, the
branching ratios turn out to be around 5 x 10(-9) for B-s --> gamma m
u(+)mu(-) and around 6 x 10(-10) for B-d --> gamma mu(+)mu(-) with sli
ghtly larger values for B-s(B-d) --> gamma e(+)e(-). The differential
rate as a function of the dilepton invariant mass is given. The possib
ility of using these processes to determine the decay constants of B-s
or B-d is discussed.