Abstract: Two per se known cross-strapping devices (10, 11) to which packages or bundles (1, 2 . . . 5) to be strapped are supplied in a conveying direction (F) in which one package or bundle at a time is positioned and crosswise strapped and out of which strapped packages or bundles are conveyed in the same conveying direction (F), are arranged in direct succession and are operated as a “tandem” by supplying two packages or bundles (1, 2), one to each one of the devices, by simultaneously strapping them and by conveying them away again simultaneously. For this purpose, a mutual control mode is necessary in which mutual control mode, in the two devices conveying steps (b) are carried out alternating with strapping steps (a) whereby the conveying stroke (2h) of the conveying steps is twice as long as when operating one only device. Compared to a single cross-strapping device, the arrangement has an increased performance and requires a minimal amount of additional space.