Double beta decay (β + EC, EC/EC) of$^{58}$Ni is investigated at France’s Modane Underground Laboratory (4800 m water equivalent) using the OBELIX ultralow-background HPGe detector with a sensitive volume of 600 cm$^{3}$ and a natural nickel sample of ~68% 58Ni with a mass of ~21.7 kg. After preliminary analysis of the experimental data accumulated over ~144 days, new experimental limits are obtained for the 2νβ$^{+}$EC decay of$^{58}$Ni to the 0$^{+}$ ground state and the 2$_{1}^{+}$ , 811 keV excited state of$^{58}$Fe, and for the 2νEC/EC decay of$^{58}$Ni to the 2$_{1}^{+}$ , 811 keV and 2$_{2}^{+}$ , 1675 keV excited states of$^{58}$Fe. The limits are T$_{1/2}$(β$^{+}$EC,0→0$^{+}$) > 1.7 × 10$^{22}$ yr, T$_{1/2}$(β$^{+}$EC,0→2$_{1}^{+}$ ) > 2.3 × 10$^{22}$ yr, T$_{1/2}$(EC/EC,0→2$_{1}^{+}$ ) > 3.3 × 10$^{22}$ yr, and T$_{1/2}$(EC/EC,0→2$_{2}^{+}$ ) > 3.4 × 10$^{22}$ yr. Experimental limit T$_{1/2}$(0νEC/EC–res, 1918 keV > 4.1 × 10$^{22}$ yr is obtained for resonant neutrinoless radiative EC/EC decay with an energy of 1918.3 keV. All limits are at 90% CL.