One-pot hydroprocessing of vegetable oils to the corresponding fatty alcohols or long-chain alkanes is highly demanded. In this work, we present results on the hydroconversion of sunflower oil in a batch stirred reactor using either CuZn oxide catalysts with different Cu/Zn ratios prepared by the calcination of hydroxycarbonate precursors or bifunctional catalysts prepared by mixing the CuZn oxides with a commercial HBEA zeolite. The characteristics of the CuZn samples were determined by N2 adsorption, N2O chemisorption, and XRD analysis. The influence of CuZn catalysts composition, reaction temperature (210–270 °C), hydrogen pressure (6.0–14.0 MPa), and catalyst loading on the conversion of sunflower oil was investigated. Under optimized conditions of 250 °C and 10 MPa H2, a nearly 89 % octadecanol yield was obtained after 3 h of sunflower oil hydroconversion using a catalyst with the Cu/Zn atomic ratio of 1. This Cu1Zn catalyst also confirmed its high stability in the production of fatty alcohols without any loss in activity after its reuse in three consecutive reaction cycles. The addition of HBEA to the Cu1Zn catalyst under the same reaction conditions led to the formation of hydrocarbons. It allowed concluding that metallic Cu species in the bifunctional catalysts were active sites for the hydrogenolysis of triglycerides to fatty alcohols and double bonds hydrogenation, while the acidic sites of HBEA were responsible for the dehydration of the produced alcohols affording hydrocarbons. As a result, n-octadecane with the yield of 65 % and a mixture of C18 alkenes and isoalkanes with the yield of 18 % were produced over the CuZn-HBEA catalyst under the same reaction conditions. It was shown that the addition of Pd to HBEA led to an increase in sunflower conversion from 90 % to 97 %.