Eucalyptus oil is available as an essential oil that is used as a medicine to treat a variety of common diseases and conditions including nasal congestion, asthma, and as a tick repellent. Diluted eucalyptus oil may also be applied to the skin as a remedy for health problems such as arthritis and skin ulcers. Peppermint contains a compound called menthol. Menthol is responsible for many of the benefits of peppermint oils. Menthol also gives peppermint its taste, smell, and cooling sensation.