Neutron capture and transmission measurements have been carried out upon 182W, 183W, 184W, 186W, 90Zr, 91Zr, 92Zr, and 94Zr over the energy range from ∼150 eV to ≤100 keV at the Rensselaer Polytechnic Institute LINAC Laboratory. Many new resonances have been observed and many resonances, reported previously as singlets, have been resolved into doublets. Most of the resonances that previously eluded observation are assigned to p-wave neutrons. Pertinent resonance parameters have been extracted from the data, and the s-wave and the p-wave strength functions of tungsten and zirconium have been determined from these parameters. The values of the s-wave strength functions in units of 10−4 are: for 182W, 2.60 ± 0.54; for 183W, 2.41 ± 0.48 per spin state; for 184W, 3.0 ± 0.6; for 186W, 2.15 ± 0.46; for 90Zr, 2.0 ± 1.4; for 91Zr, 1.2 ± 0.4 per spin state; for 92Zr, 2.6 ± 1.5, and for 94Zr, 1.0 ± 0.8. The p-wave strength functions in units of 10−4 are: for the even-even tungsten isotopes, ; for 90Zr, 7 ± 4; for 91Zr, 3 ± 2 per spin state; for 92Zr, 7 ± 5, and for 94Zr, 4 ± 2.