A pet door comprises a frame hingedly supporting a flap undersized relative to the opening therefor in the frame; the resulting gaps therebetween are weatherproofed by sealing means in part constituted by co-extensive plastics magnet strips on confronting edges of the flap and frame. One magnet strip at least is mounted for movement in a direction across the gap into and out of face-to-face sealing contact with the other magnet strip, respectively as the flap enters and leaves its closed position; the movement is responsible for jam-free closing and opening.