A system comprising an anchoring system and a stretcher, wherein the stretcher comprises a rectangular frame supporting a surface for bearing the patient and to which there are fixed two pairs of retractable legs (13d, 13t) equipped with wheels at their free ends, the anchoring system comprising: - a pair of horizontal rails coupleable to an ambulance floor; - a structure which is designed for being fixed to an ambulance floor and includes the rails; - rear retractable legs and front retractable legs which, respectively, are fixed to the frame on the lower part of the frame; wherein the free ends of the retractable legs (13t, 13d) comprise wheels which allow moving the stretcher over the floor or ground before introducing the stretcher into the ambulance; - a pair of first auxiliary wheels, wherein each first auxiliary wheel is rigidly fixed to a front end portion of a respective side bar of the frame of the stretcher, and wherein the first auxiliary wheels are slidingly coupleable in the longitudinal direction to said pair of horizontal rails, - a pair of second auxiliary wheels, wherein each second auxiliary wheel is rigidly fixed to the respective side bar of the frame of the stretcher in a position longitudinally adjacent to, and aligned with, the first auxiliary wheel fixed to the same side bar, such that the pair of second auxiliary wheels is also slidingly coupleable in the longitudinal direction to said pair of horizontal rails, the anchoring system being characterized in that the second auxiliary wheels are located in a longitudinal position between the attachment of front retractable legs to the frame of the stretcher and the position of the first auxiliary wheels, and in that the profile of the pair of horizontal rails comprises a lower horizontal segment and an upper horizontal segment separated from one another by a distance essentially equal to the diameter of the auxiliary wheels (3, 4), such that when the auxiliary wheels (3, 4) are introduced into the rails, they are confined between the lower horizontal segment and the upper horizontal segment of said rails, preventing any vertical movement thereof. - a pair of horizontal rails coupleable to an ambulance floor; - a structure which is designed for being fixed to an ambulance floor and includes the rails; - rear retractable legs and front retractable legs which, respectively, are fixed to the frame on the lower part of the frame; wherein the free ends of the retractable legs (13t, 13d) comprise wheels which allow moving the stretcher over the floor or ground before introducing the stretcher into the ambulance; - a pair of first auxiliary wheels, wherein each first auxiliary wheel is rigidly fixed to a front end portion of a respective side bar of the frame of the stretcher, and wherein the first auxiliary wheels are slidingly coupleable in the longitudinal direction to said pair of horizontal rails, - a pair of second auxiliary wheels, wherein each second auxiliary wheel is rigidly fixed to the respective side bar of the frame of the stretcher in a position longitudinally adjacent to, and aligned with, the first auxiliary wheel fixed to the same side bar, such that the pair of second auxiliary wheels is also slidingly coupleable in the longitudinal direction to said pair of horizontal rails, the anchoring system being characterized in that the second auxiliary wheels are located in a longitudinal position between the attachment of front retractable legs to the frame of the stretcher and the position of the first auxiliary wheels, and in that the profile of the pair of horizontal rails comprises a lower horizontal segment and an upper horizontal segment separated from one another by a distance essentially equal to the diameter of the auxiliary wheels (3, 4), such that when the auxiliary wheels (3, 4) are introduced into the rails, they are confined between the lower horizontal segment and the upper horizontal segment of said rails, preventing any vertical movement thereof.