The present invention provides a topical drug delivery system which comprises: a therapeutically effective amount of an anti-alopecia agent; at least one dermal penetration enhancer, which is a safe skin-tolerant ester sunscreen ester; and a volatile liquid. The invention also provides a method for administering at least one systemic acting anti-alopecia agent to an animal which comprises applying an effective amount of the anti-alopecia agent in the form of the drug delivery system of the present invention.