A pet door assembly 10 that comprises a closure assembly 11 that defines a passageway suitable for passage of an animal, the closure assembly 11 having a closure member 44 that is displaceable by an animal between open and closed positions to open and close the opening, respectively, to accommodate the passage of the animal through the opening and a circular security closure 90 that is operatively arranged with respect to the closure assembly 11 and is operable to inhibit access to the passageway. The closure assembly and the security closure include complementary formations that are configured to permit the security closure to engage or disengage with the closure assembly. The complementary formations are configured so that engagement or disengagement takes place with either rotational displacement of the circular security closure, relative to the closure assembly, to thereby inhibit or permit access to the passageway.