The hydrogenation of 5-(hydroxymethyl)furfural (HMF) to 2,5-bis(hydroxymethyl)tetrahydrofuran (DHMTHF) in aqueous media under relatively mild reaction conditions has been investigated over heterogeneous RANEY® Cu and Ni catalysts using a continuous-flow hydrogenation reactor. These RANEY® catalysts were selected following a screening of several catalysts including precious metals supported on carbon for the hydrogenation of HMF. A single-stage versus a two-stage process for the hydrogenation of HMF into DHMTHF, i.e. via 2,5-dihydroxymethylfuran (DHMF) has been evaluated. The best result with an average selectivity of 98% for DHMTHF was obtained using a two-stage process; RANEY® Cu was used as a catalyst for the highly selective hydrogenation of HMF to DHMF (92 mol%) in the first stage and this product was used without further purification for in a second-stage selective hydrogenation of DHMF into DHMTHF using RANEY® Ni as a catalyst. The influence of the HMF concentration in the feeding solution (1–3 wt%), flow rate (0.05–0.25 mL min−1) and total pressure (20–90 bar) were investigated for the first-stage hydrogenation of HMF into DHMF over RANEY® Cu. HMF was found to exert an inhibiting effect on the conversion due to strong adsorption. The RANEY® Ni catalyst used in the second stage gradually deactivated. A procedure for in situ regeneration of the partially deactivated RANEY® Ni catalyst using acetic acid washing was investigated with limited success.