A functioning method for a continuous pressing device of products containing a solid part and a liquid part, wherein the device comprises: - a tubular body having a lateral wall at least a portion of which is perforated, - a piston (485, 600) slidably inserted in a first end of the tubular body, - a pressing chamber defined internally of the tubular body between an end face of the piston (485, 600) and a second axial end of the tubular body; - at least an inlet mouth afforded in the body of the piston (485, 600) and opening into the pressing chamber through the end face of the piston (485, 600); - a pump connected to the inlet mouth for supplying the product to be pressed internally of the pressing chamber and - obturator means for opposing exit of the product from the second axial end of the tubular body, the obturator means being able to move between a position of complete closure of the pressing chamber, in which the obturator means prevent outlet of the product, and a position of complete opening of the pressing chamber, in which the obturator means enable the product to exit freely, - a scraper ring or scraper cylinder (495, 615), which is coaxially inserted in the tubular body and is able to move alternatingly with respect to both the tubular body and the piston (485, 600), wherein the functioning method comprises a start-up step which comprises: - predisposing the obturator means in a position of complete closure, - starting up the pump so as to load the product to be pressed in the pressing chamber up to forming a compact agglomeration of pressed product at the second axial end of the tubular body, - displacing the obturator means into a position of at least partial opening of the pressing chamber, and then a successive step of continuous-cycle pressing which comprises: - maintaining the pump in constant function, in such a way as to continuously supply the product to be pressed internally of the pressing chamber and such as to cause consequent outlet of the pressed product from the second end of the tubular body. - a tubular body having a lateral wall at least a portion of which is perforated, - a piston (485, 600) slidably inserted in a first end of the tubular body, - a pressing chamber defined internally of the tubular body between an end face of the piston (485, 600) and a second axial end of the tubular body; - at least an inlet mouth afforded in the body of the piston (485, 600) and opening into the pressing chamber through the end face of the piston (485, 600); - a pump connected to the inlet mouth for supplying the product to be pressed internally of the pressing chamber and - obturator means for opposing exit of the product from the second axial end of the tubular body, the obturator means being able to move between a position of complete closure of the pressing chamber, in which the obturator means prevent outlet of the product, and a position of complete opening of the pressing chamber, in which the obturator means enable the product to exit freely, - a scraper ring or scraper cylinder (495, 615), which is coaxially inserted in the tubular body and is able to move alternatingly with respect to both the tubular body and the piston (485, 600), - predisposing the obturator means in a position of complete closure, - starting up the pump so as to load the product to be pressed in the pressing chamber up to forming a compact agglomeration of pressed product at the second axial end of the tubular body, - displacing the obturator means into a position of at least partial opening of the pressing chamber, - maintaining the pump in constant function, in such a way as to continuously supply the product to be pressed internally of the pressing chamber and such as to cause consequent outlet of the pressed product from the second end of the tubular body.