Abstract: A methanol-synthesis reactor has a housing receiving a catalyst packing and coils of cooling tubes surrounding a core tube and disposed in helical radially spaced layers coaxial with the core tube. According to the invention, the internal diameters of the cooling tubes are from 4 to 50 mm, the distance between neighboring tubes in a direction transverse to the axis and the direction of fluid flow through the catalyst packing is between 2 and 20 times the smallest longitudinal dimension of the catalyst particles and the distance between neighboring tubes measured in the direction of the synthesis gas flow is less than 10 times the transverse distance.