We report on the extraction of R=sigma_L/sigma_T from CCFR nu_mu-Fe and nubar_mu-Fe differential cross sections. The CCFR differential cross sections do not show the deviations from the QCD expectations that are seen in the CDHSW data at very low and very high x. R as measured in nu_mu scattering is in agreement with R as measured in muon and electron scattering. All data on R for Q^2 > 1 GeV^2 are in agreement with a NNLO QCD calculation which includes target mass effects. We report on the first measurements of R in the low x and Q^2 < 1 GeV^2 region (where an anomalous large rise in R for nuclear targets has been observed by the HERMES collaboration).