An anti-flooding safety device includes two connection bodies, a valve arrangement that includes a valve member, a retention member for withholding the valve member in a respective opening position, and an inner hose and an outer hose impermeable to water. The inner hose hydraulically connects the two connection bodies and extends at least in part within the outer hose so that defined between the two hoses is a gap designed to withhold inside it any possible leaking water. A connection body has a control chamber that is at least in part delimited by a movable element, and a control member is coupled to the movable element so that a displacement of the latter will cause a displacement of the control member towards a respective position of release, wherein the valve member is free to pass into its closing position. The gap is in fluid communication with the control chamber, to obtain a substantially closed volume therewith.