The study will examine if ONO-6950 could alleviate EAR and LAR caused by an allergen challenge in subjects with asthma. Patients will be required to have EAR and LAR after standardized allergen challenges during the screening. Eligible patients will complete a randomized, double-blind, three-way crossover study. During each of three evaluation periods, patients will be administered either 200 mg ONO-6950, 10 mg Montelukast, or placebo for 8 days. Each evaluation period will occur over 8 days and will include various assessments following allergen challenge and methacholine challenge. The study does not require an overnight stay at the clinical research center.