A flexible package-forming machine for horizontal packaging by folding and welding flexible band comprising, in this order with respect to a forward movement direction of the flexible band, at least: • one unwinding unit for unwinding the flexible band in the forward movement direction; • one perforating unit of the flexible band for perforating the flexible band in pre-established precise positions thereof; • one folding unit of the flexible band configured for folding said flexible band along at least one folding line parallel to the forward movement direction, at least two portions arranged on opposite sides of said at least one folding line of one and the same face of the flexible band being arranged opposite one another; • one welding unit of the folded flexible band configured for making welding lines at least in a direction transverse to the forward movement direction of the flexible band; • one cutting unit for separating portions making up flexible packages; characterized in that a movement compensating unit for compensating the movement of the flexible band intercalated between the perforating unit and the folding unit, said compensating unit linking a section with intermittent forward movement of the flexible band and a section with continuous forward movement of the flexible band, said compensating unit being provided with at least: • one inlet roller in contact with the flexible band with an axis of rotation perpendicular to the forward movement direction and fixed with respect to the forming machine, • one outlet roller in contact with the flexible band with an axis of rotation perpendicular to the forward movement direction and fixed with respect to the forming machine; • at least one accumulator roller in contact with the flexible band between the inlet roller and the outlet roller in the forward movement direction, and with an axis of rotation perpendicular to the forward movement direction and movable with respect to the axes of rotation of the inlet roller and the outlet roller being kept perpendicular to the forward movement direction of the flexible band; said accumulator roller being provided with and/or connected to a tautening device provided for moving the accumulator roller away from the inlet roller and/or outlet roller, keeping the flexible band taut; and wherein the section with intermittent forward movement includes an intermittent drive unit configured for moving the flexible band in the forward movement direction in an intermittent manner, and wherein the section with continuous forward movement includes a continuous drive unit configured for moving the flexible band in the forward movement direction in a continuous manner. • one unwinding unit for unwinding the flexible band in the forward movement direction; • one perforating unit of the flexible band for perforating the flexible band in pre-established precise positions thereof; • one folding unit of the flexible band configured for folding said flexible band along at least one folding line parallel to the forward movement direction, at least two portions arranged on opposite sides of said at least one folding line of one and the same face of the flexible band being arranged opposite one another; • one welding unit of the folded flexible band configured for making welding lines at least in a direction transverse to the forward movement direction of the flexible band; • one cutting unit for separating portions making up flexible packages; • one inlet roller in contact with the flexible band with an axis of rotation perpendicular to the forward movement direction and fixed with respect to the forming machine, • one outlet roller in contact with the flexible band with an axis of rotation perpendicular to the forward movement direction and fixed with respect to the forming machine; • at least one accumulator roller in contact with the flexible band between the inlet roller and the outlet roller in the forward movement direction, and with an axis of rotation perpendicular to the forward movement direction and movable with respect to the axes of rotation of the inlet roller and the outlet roller being kept perpendicular to the forward movement direction of the flexible band;