Inclusion Criteria:

• Patient has a current diagnosis of OSAHS and has a complaint of excessive sleepiness despite effective nCPAP therapy.
• Patient has excessive sleepiness as evidenced by a mean sleep latency of less than 8 minutes, as determined by the MSLT.
• Patient has an ESS score of 10 or more at the initial screening visit.
• Patient has a habitual sleep time beginning no earlier than 2100 and ending no later than 0700.
• Patient is right-handed. Patients who are ambidextrous may be eligible following consultation with the medical monitor.
• Women of childbearing potential must use a medically accepted method of contraception and must agree to continue use of this method for the duration of the study and for 30 days after participation in the study.
• Patient exhibits reasonable accuracy (≥80%) on the 2-back working memory task during the training session at the second screening visit.

Exclusion Criteria:

The Patient:

• The patient is a current smoker or has a prior history of smoking (defined as ≥1 pack-year) within 2 years prior to the screening visit.
• consumes caffeine including coffee, tea and/or other caffeine-containing beverages or food averaging more than 400 mg of caffeine per day (approximately equivalent to 4 or more cups of coffee).
• has NART-predicted verbal IQ and QIDS-SR16 scores within protocol-specific exclusionary ranges.
• has a clinically significant, uncontrolled medical or psychiatric conditions (treated or untreated).
• has a confirmed or probable diagnosis of a current sleep disorder other than OSAHS.
• has used any excluded prescription drugs or procedures for prohibited and allowed drugs within the excluded timeframe.
• has a history of alcohol, narcotic, or any other drug abuse.
• has a positive UDS, without medical explanation, at the screening visit.
• has a clinically significant deviation from normal in the physical examination.
• is a pregnant or lactating woman. Any woman becoming pregnant during the study will be withdrawn from the study.
• has a past or present seizure disorder, head trauma that is clinically significant, or past neurosurgery.
• has used an investigational drug within 1 month before the screening visit.
• has any disorder that may interfere with drug absorption, distribution, metabolism, or excretion (including gastrointestinal surgery).
• has a known hypersensitivity to armodafinil or modafinil, or any other component of the study drug tablets.
• has a history of any clinically significant cutaneous drug reaction, or a history of clinically significant hypersensitivity reaction, including multiple allergies or drug reactions.
• has known human immunodeficiency virus (HIV).
• has clinical laboratory test value(s) outside the range(s) specified in the Protocol, or presents a clinically significant laboratory abnormality without prior written approval by the medical monitor.
• has worked the night shift within 28 days of the baseline visit, or will work the night shift during the double-blind segment of the study.
• anticipates any travel across more than 3 time zones at any time during the study.
• needs to use any of the excluded medications identified in this protocol.
• is unable to complete neuroimaging studies, performance tasks, self-rating scales, and all other study assessments.
• has a contraindication to fMRI scanning, (such as an implanted pacemaker/defibrillator, aneurysm clips, drug infusion device or metallic foreign body).
• is suspected to be unable to tolerate fMRI scanning (eg, claustrophobic) and/or the testing paradigm.
• has physical or other characteristics that suggest imaging data will be unobtainable or degraded.