Beam-foil quantum-beat techniques have been used to measure the 3D1-3D2 intervals of 1snd (n=3-8) in 4He. I. A two-spectrometer technique was used as to obtain simultaneously a time calibration from the 1s3p(3P1-3P2) fine-structure separation. The following 3D1-3D2 separations (in MHz) were found: 1323.62.3 (n=3), 553.0+or-0.7 (n=4), 284.1+or-0.6 (n=5), 165.3+or-1.0 (n=6), 101.6+or-1.1 (n=7) and 69+or-3 (n=8). These results are compared with previous measurements and theoretical values.