System for cremating the deceased and the cremation of exhumed corpses, having a carriage in order to be moved and transferred in block and used on any site, wherein - it includes a funerary cell to receive and preserve temporarily a deceased person, where said funerary cell includes a coffin - it comprises, in combination a cremation chamber, an afterburner, a filtering group for filtering the effluent fumes from the afterburner, a fan for the circulation of the gaseous fluids and control devices of the process to be carried out; - it is installed on a depressed deck of a vehicle, in particular a semi-trailer, connectable to a tractor; - it comprises an electric generator and a fuel reserve tank to autonomously feed the process to be carried out; characterized in that the system further comprises a fumes/air exchanger and in that said coffin further comprises a folding cover and a covering in the form of a container or waterproof bag with at least a longitudinal means for closing and able to contain and hold the body, wherein a first lateral wall of the coffin can be opened enabling the enclosed body to be extracted from the side at the moment to be inserted into a cremation system, without the coffin; - the cover of the coffin is hinged to a second lateral wall of the coffin, opposite the first lateral wall, and connected to an auxiliary system to facilitate and maintain its open position, and in that the first wall is a longitudinal folding wall on one side compared with the bottom; and - the waterproof covering is configured for a disposition, starting from a flat folded condition, to an open unfolded condition to cover the inside of the coffin when the latter is open for the exposition of the body of the deceased person and a closed condition with a three-dimensional set up of containers for its use, said covering being equipped with at least one longitudinal zip to close it in the shape of a container. - it includes a funerary cell to receive and preserve temporarily a deceased person, where said funerary cell includes a coffin - it comprises, in combination a cremation chamber, an afterburner, a filtering group for filtering the effluent fumes from the afterburner, a fan for the circulation of the gaseous fluids and control devices of the process to be carried out; - it is installed on a depressed deck of a vehicle, in particular a semi-trailer, connectable to a tractor; - it comprises an electric generator and a fuel reserve tank to autonomously feed the process to be carried out; characterized in that the system further comprises a fumes/air exchanger and in that said coffin further comprises a folding cover and a covering in the form of a container or waterproof bag with at least a longitudinal means for closing and able to contain and hold the body, wherein a first lateral wall of the coffin can be opened enabling the enclosed body to be extracted from the side at the moment to be inserted into a cremation system, without the coffin; - the cover of the coffin is hinged to a second lateral wall of the coffin, opposite the first lateral wall, and connected to an auxiliary system to facilitate and maintain its open position, and in that the first wall is a longitudinal folding wall on one side compared with the bottom; and - the waterproof covering is configured for a disposition, starting from a flat folded condition, to an open unfolded condition to cover the inside of the coffin when the latter is open for the exposition of the body of the deceased person and a closed condition with a three-dimensional set up of containers for its use, said covering being equipped with at least one longitudinal zip to close it in the shape of a container.