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The atomic-beam laser-rf double-resonance technique has been used to make precision measurements of the hyperfine structure (hfs) splittings in the 5${\mathit{d}}^{2}$6${\mathit{s}}^{2}$ $^{3}$${\mathit{F}}_{\mathit{J}}$ (J=2\char21{}4) states in $^{177,179}\mathrm{Hf}$ i. By making corrections to the second-order hfs effects, magnetic dipole (A), electric quadrupole (B), and magnetic octupole (C) hfs constants are obtained for the $^{3}$${\mathit{F}}_{\mathit{J}}$ states in $^{177,179}\mathrm{Hf}$: The constant C has a strong J dependence as well as does A and B; the isotopic ratio of the constant A between $^{177}\mathrm{Hf}$ and $^{179}\mathrm{Hf}$ has a significant J dependence, indicating J-dependent hyperfine anomalies, while that of the constant C is independent of J within experimental uncertainties, which is taken to be the ratio of the nuclear-ground-state magnetic octupole moments \ensuremath{\Omega}, i.e., \ensuremath{\Omega}${(}^{177}$Hf)/\ensuremath{\Omega}${(}^{179}$Hf)=-0.41(9). It is also pointed out that there is a clear indication of nuclear-spin dependence of the isotopic ratios of C. The single-electron hfs parameters of the 5d electron for the 5${\mathit{d}}^{2}$6${\mathit{s}}^{2}$ configuration in Hf i are obtained, and the Sternheimer shielding factor ${\mathit{R}}_{5\mathit{d}}$=-0.397(8) is derived.

Hyperfine structure of the 5${\mathit{d}}^{3}$6${\mathit{s}}^{2}$ $^{4}$${\mathit{F}}_{3/2}$ ground state in $^{180\mathit{m}}\mathrm{Ta}$ i was precisely measured by means of atomic-beam laser-rf double-resonance spectroscopy. Hyperfine-interaction constants A and B for the ground state $^{4}$${\mathit{F}}_{3/2}$ were determined with accuracies of 3 and 10 ppm, respectively. The nuclear electric quadrupole moment was derived, as well as a precise value of the magnetic moment for $^{180\mathit{m}}\mathrm{Ta}$ (${\mathit{I}}^{\mathrm{\ensuremath{\pi}}}$=${9}^{\mathrm{\ensuremath{-}}}$): the magnetic dipole moment is ${\mathrm{\ensuremath{\mu}}}_{\mathit{I}}^{180\mathit{m}}$=+4.825(11)${\mathrm{\ensuremath{\mu}}}_{\mathit{N}}$ and the spectroscopic quadrupole moment is ${\mathit{Q}}_{\mathit{s}}^{180\mathit{m}}$=+4.946(20)b.