The ratio of the deuteron to proton structure functions is measured at very small Bjorken {ital x} (down to 10{sup --6}) and for {ital Q}{sup 2}{gt}0.001 GeV{sup 2} from scattering of 470 GeV muons on liquid hydrogen and deuterium targets. The ratio {ital F}{sup {ital n}}{sub 2}/{ital F}{sup {ital p}}{sub 2} extracted from these measurements is found to be constant, at a value of 0.935{plus_minus}0.008{plus_minus}0.034, for {ital x}{lt}0.01. This result suggests the presence of nuclear shadowing effects in the deuteron. The dependence of the ratio on {ital Q}{sup 2} is also examined; no significant variation is found.
