Generally, compositions which can be applied to hair, fur or skin of an animal and are useful for reducing, removing or eliminating undesirable materials or odors or parasites (“extraneous matter”) from the hair, fur or skin of the animal. Specifically, compositions which can be applied to hair, fur or skin of an animal and can reduce, remove or eliminate undesirable materials or odors or parasites (“extraneous matter”) from the hair, fur or skin of the animal without a need of a rinse composition.