A process of producing a porous-polytetrafluoroethylene-membrane composite in which the pore diameter continuously increases or decreases in the direction of the thickness from one side of the membrane toward the other side and the mean flow pore diameter is 50 nm or less, the process comprising: a step 1 of forming a nonporous fluororesin membrane by casting, onto a smooth foil, a fluororesin dispersion produced through dispersing, into a dispersion medium, a powder of fluororesin containing at least 50 mass% polytetrafluoroethylene, subsequently by evaporating the dispersion medium, and then by performing heating to the melting point of the fluororesin or above to perform baking; a step 2 of forming another nonporous fluororesin membrane by casting, onto the nonporous fluororesin membrane formed in the step 1, a fluororesin dispersion produced through dispersing, into a dispersion medium, a powder of fluororesin containing at least 50 mass% polytetrafluoroethylene having a different quantity of heat of fusion from that of the polytetrafluoroethylene used in the step 1, subsequently by evaporating the dispersion medium, and then by performing heating to the melting point of the fluororesin or above to perform baking; a step 3 of bonding a porous supporter with the nonporous fluororesin membrane at the outermost layer, the step 3 being performed after repeating the step 2 as necessary, wherein when step 2 is repeated, the quantity of heat of fusion of the PTFE used in each of the steps is different from each other, and every time the step 2 is repeated, the step is performed such that the quantity of heat of fusion is increased or decreased to produce a multilayered nonporous fluororesin membrane in which the quantity of heat of fusion of the PTFE increases or decreases in the direction of the thickness from one side of the membrane toward the other side; a step 4 of removing the smooth foil to obtain a composite having a multilayered nonporous fluororesin membrane, the step 4 being performed after the step 3; and a step 5 of stretching the composite, the step 5 being performed after the step 4. a step 1 of forming a nonporous fluororesin membrane by casting, onto a smooth foil, a fluororesin dispersion produced through dispersing, into a dispersion medium, a powder of fluororesin containing at least 50 mass% polytetrafluoroethylene, subsequently by evaporating the dispersion medium, and then by performing heating to the melting point of the fluororesin or above to perform baking; a step 2 of forming another nonporous fluororesin membrane by casting, onto the nonporous fluororesin membrane formed in the step 1, a fluororesin dispersion produced through dispersing, into a dispersion medium, a powder of fluororesin containing at least 50 mass% polytetrafluoroethylene having a different quantity of heat of fusion from that of the polytetrafluoroethylene used in the step 1, subsequently by evaporating the dispersion medium, and then by performing heating to the melting point of the fluororesin or above to perform baking; a step 3 of bonding a porous supporter with the nonporous fluororesin membrane at the outermost layer, the step 3 being performed after repeating the step 2 as necessary, wherein when step 2 is repeated, the quantity of heat of fusion of the PTFE used in each of the steps is different from each other, and every time the step 2 is repeated, the step is performed such that the quantity of heat of fusion is increased or decreased to produce a multilayered nonporous fluororesin membrane in which the quantity of heat of fusion of the PTFE increases or decreases in the direction of the thickness from one side of the membrane toward the other side; a step 4 of removing the smooth foil to obtain a composite having a multilayered nonporous fluororesin membrane, the step 4 being performed after the step 3; and a step 5 of stretching the composite, the step 5 being performed after the step 4.