A surgical access assembly for use with a surgical access device includes a housing defining a central longitudinal axis, an elongate access member extending from the housing whereby the housing and the access member having a longitudinal passage dimensioned to permit passage of a surgical instrument, an instrument seal disposed within the housing and being adapted to establish a substantial fluid tight seal about the instrument and a zero closure valve mounted relative to the housing and being adapted to assume an open condition upon passage of the surgical instrument and a substantially closed position in the absence of the instrument. The zero closure valve includes a valve periphery and first and second lips depending from the valve periphery. The first and second lips have lip edge surfaces in juxtaposed relation to define a slit when the valve is in the closed position thereof. At least one of the lips has a general arcuate internal lip surface leading to the lip edge surface to define a sloping configuration dimensioned to facilitate passage of the surgical instrument through the valve. Each of the first and second lips may define a general arcuate lip surface. In one embodiment, the internal arcuate lip surface of each of the first and second lips includes an outer surface portion arranged at a first angle relative to the longitudinal axis of the seal housing and an inner surface portion arranged at a second angle relative to longitudinal axis and being different from the first angle. The first angle is greater than the second angle.