We study the impact of the nuclear dependence of R = σL/σT on the extraction of the F A 2 /F D 2 and F A 1 /F D 1 structure function ratios from the data on the σ A /σ D cross section ratios. Guided by indications of the nuclear dependence of R from the world data, we examine selected sets of EMC, BCDMS, NMC and SLAC data and find thatIn particular, we observe that the nuclear enhancement (antishadowing) for F A 1 /F D 1 in the interval 0.1 < x < 0.3 becomes significantly reduced or even disappears, which indicates that antishadowing is dominated by the longitudinal structure function FL. We also argue that precise measurements of nuclear modifications of R and F A L have the potential to constrain the poorly known gluon distribution in nuclei over a wide range of x.