This trial will examine the efficacy and safety of 5 mg/kg doses of infliximab in patients with inhaled corticosteroid-dependent asthma. The primary objective of this study is to obtain pharmacological evidence for a role of the pro-inflammatory cytokine TNF-alpha in patients with asthma symptomatic on inhaled steroids and to evaluate the safety and tolerability of repeated intravenous administration of infliximab.