This device includes anchoring mechanism being actuated by a rope and fitted to respective attachments being provided on the pram. The device has two portions namely being a first one (1) being provided at the lower end of the handle and having a cavity (5) in an angularly tiltable arrangement housing an action element (6) being fit to act on the anchoring mechanism (7), and a second portion (2) being solid with the carrycot seat (4) or carrycot and including the anchoring mechanism (7). The action element (6) is made up by an arcuate part one (6′) of whose ends is arranged in a pivoting arrangement at the angular end (5′) of the cavity (5), the arcuate part being at its other end (6″) linked to the pulling rope (8). The action element (6) is fit to act on the bent upper end (9) of a rod (10) pertaining to the anchoring mechanism (7).