This study will be conducted in two cohorts running in parallel: Cohort A will evaluate the safety, tolerability, and efficacy of inhaled AP-PA02 in subjects who have not received an antipseudomonal inhaled antibiotic for a minimum of 3 months prior. Cohort B will evaluate the safety, tolerability, and efficacy of inhaled AP-PA02 in subjects who have received an antipseudomonal inhaled antibiotic for a minimum of 3 months prior. Subjects in both Cohorts A and B will be followed for approximately 4 weeks after last dose of study drug and evaluated for safety, tolerability, and efficacy.