The cross sections for (n,x) reactions with Lu, Tb, and Ta isotopes were measured at (d,t) neutron energies around 14 MeV with the activation technique using metal foils of natural composition. Additionally, tantalum samples were irradiated with (d,d) neutrons and filtered neutron beams. To ensure an acceptable precision of the results all major sources of uncertainties were taken into account. Calculations of efficiency and correction factors were performed with the Monte Carlo technique. The cross section results obtained for the 175 Lu(n,α) 172 Tm reaction at (d,t) neutron energies are reported for the first time. 181 Ta(n,γ ) 182 Ta m2 reaction cross sections were also measured for the first time at 1.9, 58.7, and 144.3 keV and at 2.85 MeV. The earlier evaluated cross section upper estimate for the nuclear reaction 159 Tb(n,n α) 155 Eu is reported in this article to be one order lower. Some other cross sections were obtained with higher precision. Theoretical calculations of excitation functions were performed with the TALYS-1.0 code and compared with the experimental cross section values.