A closure for a valve (128) of a connector (100) of a haemostatic valve assembly comprises a resilient closure member (130), which defines a first and a second, opposite end surface (156; 160) and at least one passage slit (164). The passage slit is normally closed and extends between the two end surfaces, the passage slit being arranged to open by a tubular member (134) being extended therethrough, the passage slit (164) having a wider extent at the first surface than at the second surface. A plurality of such passage slits (164) may define a first, common point of contact (166) on the first surface (156) and may extend radially outwardly from the point of contact (166) at the first surface (156).