A unit for carrying out an operation on a container fillable with a pourable product under aseptic conditions, comprising: - a first non-aseptic area; - a second aseptic area; - at least one operative head (10, 21), which is adapted to carry out said operation; and - at least one gripping device for gripping said container and which is movable between: a lowered rest position, in which it receives or discharges said container; and a raised operative position, in which it sets said container in a position in which said container undergoes, in use, said operation; said unit further comprising: - a movable element, which is operatively connected to said gripping device for moving said gripping device between said lowered rest position and said raised operative position, and which comprises a portion movable between said first area and said second area; - a bellow, which is arranged inside said second area and fluid-tightly houses said portion of said movable element; and - a connecting element, which comprises, in turn,: said movable element, which moves along a first axis; a housing, which slidably houses at least said portion of said movable element; and a plate, which is connected to both said movable element and said gripping device; said bellow being interposed between said housing and said plate; said bellow being arranged on the opposite side of said gripping device with respect to said operative head (10, 21); said bellow being arranged below said gripping device and below, in use, a mouth of said container; characterized in that said bellow comprises: - a first end fixed to said housing of said movable element; and - a second end, opposite to said first end and fixed to said plate; said first end being arranged above said second end; said movable gripping device being in said operative raised position and said bellow assuming its minimum length, when said movable element is arranged in said uppermost position; said movable gripping device being in said rest lowered position and said bellow assuming its maximum length, when said movable element is arranged in said lowermost position. - a first non-aseptic area; - a second aseptic area; - at least one operative head (10, 21), which is adapted to carry out said operation; and - at least one gripping device for gripping said container and which is movable between: a lowered rest position, in which it receives or discharges said container; and a raised operative position, in which it sets said container in a position in which said container undergoes, in use, said operation; a lowered rest position, in which it receives or discharges said container; and a raised operative position, in which it sets said container in a position in which said container undergoes, in use, said operation; - a movable element, which is operatively connected to said gripping device for moving said gripping device between said lowered rest position and said raised operative position, and which comprises a portion movable between said first area and said second area; - a bellow, which is arranged inside said second area and fluid-tightly houses said portion of said movable element; and - a connecting element, which comprises, in turn,: said movable element, which moves along a first axis; a housing, which slidably houses at least said portion of said movable element; and a plate, which is connected to both said movable element and said gripping device; said bellow being interposed between said housing and said plate; said bellow being arranged on the opposite side of said gripping device with respect to said operative head (10, 21); said bellow being arranged below said gripping device and below, in use, a mouth of said container; said movable element, which moves along a first axis; a housing, which slidably houses at least said portion of said movable element; and a plate, which is connected to both said movable element and said gripping device; said bellow being interposed between said housing and said plate; said bellow being arranged on the opposite side of said gripping device with respect to said operative head (10, 21); said bellow being arranged below said gripping device and below, in use, a mouth of said container; - a first end fixed to said housing of said movable element; and - a second end, opposite to said first end and fixed to said plate; said first end being arranged above said second end; said movable gripping device being in said operative raised position and said bellow assuming its minimum length, when said movable element is arranged in said uppermost position; said movable gripping device being in said rest lowered position and said bellow assuming its maximum length, when said movable element is arranged in said lowermost position.