This study will evaluate the effect of roflumilast 500 μg once daily (QD) plus montelukast 10 mg QD versus 10 mg montelukast QD alone on predose (trough) prebronchodilator forced expiratory volume in the first second (FEV1).

The drug being tested in this study is called roflumilast. Roflumilast is being tested to treat people who have asthma. This study will look at lung function and asthma symptoms of people who take roflumilast in combination with montelukast.

Inclusion Criteria:

1. In the opinion of the investigator, the participant is capable of understanding and complying with protocol requirements (ie, to follow clinical trial procedures and Investigator instructions adequately).
2. The participant or, when applicable, the participant's legally acceptable representative signs and dates a written, informed consent form and any required privacy authorization prior to the initiation of any study procedures.
3. Has a documented physician diagnosis of severe asthma consistent with global initiative for asthma (GINA) step 4 clinical features [Gina 2011] for at least 6 months.
4. Is male or female and aged 18 years or above.
5. Has been treated with a fixed or free combination of at least medium-dose inhaled corticosteroid (ICS) (ie, ≥ 250 µg fluticasone propionate daily or equivalent ICS) plus long-acting beta agonist (LABA) for at least 3 months prior to Screening with stable ICS dose for at least 4 weeks before Visit 2.
6. Shows GINA-defined uncontrolled asthma or an asthma control questionnaire (ACQ-7) score ≥1.5 despite at least medium dose ICS/LABA therapy within 4 weeks prior to Visit 1 (Screening).
7. Shows a pre-bronchodilator FEV1 of > 55% and ≤ 85% of predicted at Visit 1 (Screening). For participants performing induced sputum FEV1 must be in addition > 1 liter.
8. Has airway obstruction proven to be reversible by an improvement of FEV1 of at least 12% and 200 mL after inhalation of a short-acting bronchodilator. This can be either documented in the medical history (with supporting spirometry recordings) in the previous 12 months or demonstrated during screening at Visit 1 (Screening).

Exclusion Criteria:

1. Has received any investigational compound within 30 days prior to the start of the clinical trial or has participated in the active treatment phase of another clinical trial where a persisting pharmacodynamic effect of the trial treatment of that clinical trial cannot be excluded (eg, participant is well into a treatment free follow-up phase).
2. Participation in another clinical trial during the current trial.
3. Is an immediate family member, study site employee, or is in a dependent relationship with a study site employee who is involved in conduct of this study (eg, spouse, parent, child, sibling) or may consent under duress.
4. Severe asthma exacerbation not resolved 4 weeks prior to Visit 1, (defined by the need for oral or parenteral glucocorticosteroid intake for at least 3 days and/or hospitalization or emergency room visit with the need for oral or parenteral corticosteroid use).
5. Lower respiratory tract infection not resolved 4 weeks prior to Visit 1.
6. A diagnosis of chronic obstructive pulmonary disease (COPD) (based on Global Initiative for Chronic Obstructive Lung Disease [GOLD] criteria) and/or other relevant forms of lung disease (eg, history of primary bronchiectasis, cystic fibrosis, idiopathic (pan)bronchiolitis or bronchiolitis obliterans, bronchopulmonary allergic aspergillosis, Churg-Strauss Syndrome, paradoxical vocal cord closure, lung resection, lung cancer, interstitial lung disease [eg, fibrosis, silicosis, sarcoidosis], or active tuberculosis) that may interfere with the evaluation of a treatment response.
7. Current participation in a pulmonary rehabilitation program or completion of a pulmonary rehabilitation program within 3 months preceding Visit 1.
8. Has, in the judgment of the investigator, clinically significant abnormal laboratory values (hematology or biochemistry) at screening suggesting an undiagnosed disease requiring further clinical evaluation.
9. Has severe neuropsychiatric or neurological disorders (eg, history of depression associated with suicidal thinking, suicidal ideation or behavior).
10. Has congestive heart failure severity grade III or IV according to the New York Heart Association.
11. Has symptomatic ischemic heart disease (angina pectoris).
12. Has hemodynamically significant cardiac arrhythmias or heart valve deformations.
13. Has liver impairment, defined as Child-Pugh B/C and/or active viral hepatitis.
14. Has severe immunological diseases (eg, multiple sclerosis, systemic lupus erythematosus, progressive multifocal leukoencephalopathy) or known infection with human immunodeficiency virus (HIV).
15. Has severe acute infectious diseases (eg, tuberculosis, or acute hepatitis).
16. Has any diagnosis of a malignant disease (other than basal or squamous cell carcinoma) within 5 years prior to Screening Visit 1.
17. Has a history of smoking within 1 year of Visit 1 and smoking history ≥10 pack years.
18. Has a history of drug abuse (defined as illicit drug use) or a history of alcohol abuse (defined as regular or daily consumption of more than 2 alcoholic drinks per day) within the past 1 year prior to the Screening visit.
19. Has history of clinically significant allergies or idiosyncrasies to roflumilast, montelukast or any inactive ingredient(s) of these products, eg, rare hereditary problems of galactose intolerance, the Lapp lactase deficiency, glucose-galactose malabsorption or phenylketonuria.
20. Has known highly unstable asthma defined by severe bronchoconstriction after bronchoprovocation with isotonic saline.
21. Females of childbearing potential not willing to use acceptable contraceptive methods such as hormonal contraceptives (oral, injection or implant) or intrauterine contraceptive devices or who started such methods less than 2 months prior to screening or who are not willing to use a double barrier method of contraception (diaphragm plus condom).
22. If female, is pregnant or lactating or intending to become pregnant before, during, or within 1 month after participating in this study; or intending to donate ova during such time period.
23. Is required to take excluded medication.

Full analysis set: All randomized participants, analyzed according to the randomized treatment.

Baseline to the end of the study (Days 1-105)

Safety analysis set: All randomized participants who received at least 1 dose of study drug. Adverse events are reported for 61 and 62 participants in the roflumilast + montelukast (R+M) and placebo + montelukast (P+M) groups, respectively, as 3 participants discontinued prior to receiving R+M and 2 participants discontinued prior to receiving P+M.