There is currently no effective way to prevent development of allergic rhinitis (nasal allergies) and asthma and no cure. Sublingual immunotherapy (SLIT), a type of therapy in which allergens are placed under the tongue, may be a way to control and possibly prevent allergic rhinitis and asthma. However, detailed research of this approach is limited. The purpose of this study is to evaluate the safety and efficacy of a sublingual cockroach extract given to adults with perennial allergic rhinitis, asthma, or both.