Valves having a sprung gate of various constructions are disclosed. In one embodiment, the sprung gate includes a first endless elastic band having an inner perimeter defining an open space sandwiched between a first gate member and a second gate member that each define an opening therethrough in an open position portion thereof. The first endless elastic band is sandwiched therebetween with its open space oriented for alignment with the opening in both of the first and second gate members, which are aligned with one another to form a passage through the sprung gate. In one aspect, the first endless elastic band in positioned inward a distance from the outer sides of the first and second gate members and spaces the first gate member a distance apart from the second gate member thereby defining a channel having a bottom defined by the first endless elastic band.