A tamper evident hinge type closure includes, as is conventional in such closures, a body portion, a lid portion and a hinge portion. Advantageously, at least one tamper evident band is provided so as to mechanically secure the lid portion to the body portion at a position that is distal from the hinge. The tamper evident band, which is designed to break upon initial opening of the closure by a consumer, is preferably integral with both the body portion and the lid portion, so as to ensure more reliably than was possible with interlocking mechanical tamper evident structures that the closure may not be opened without defeating the tamper evident band. A process for making the improved closures is also disclosed.