The National Institutes of Health (NIH) has a formal appeals process to resolve disagreements between grant applicants and NIH review committees and/or NIH staff concerning the referral and peer review of grant applications. The NOT-OD-11-064: Appeals of NIH Initial Peer Review dated April 15, 2011 provides full information on the NIH policy on "Appeals of Scientific Peer Review". 

The NIH Guide Notice defines an appeal as a written communication from a Program Director/Principal Investigator (PD/PI) and/or applicant institution that meets the following four criteria: 1) is received after issuance of the summary statement and up to 30 calendar days after the second level of peer review, 2) describes a flaw or perceived flaw in the review process for a particular application, 3) is based on one or more of four allowable issues (described in the announcement), and 4) displays concurrence from the Authorized Organization Representative (AOR). 
Before beginning the appeal process, the principal investigator is strongly advised to speak with their National Institute on Alcohol Abuse and Alcoholism (NIAAA) program officer, who is listed on the summary statement. The program officer can explain the options and their consequences and is often in a position to help the applicant understand the study section's comments and recommendation. In most cases, peer review issues can be resolved at this stage.
For those cases that cannot be resolved by discussion, the first step is the submission of an appeal letter.
An appeal letter with concurrence from the institutional AOR submitted after study section review should be sent to the program officer in NIAAA. Program and review staff will try to resolve the issues and take the appropriate action. If the issues cannot be resolved by staff, the appeal letter and all relevant information are submitted to the Appeals Officer/Director of the Office of Extramural Activities, NIAAA six weeks before the next Council meeting. The documents are forwarded to the Council Executive Secretary for review by the Members of the National Advisory Council on Alcohol Abuse and Alcoholism.
If review staff and program staff do not support the appeal, or do not agree on its merit, and the appeal letter is not withdrawn, the appeal letter will be made available to Council. The IC may not deny the PD/PI or applicant organization the opportunity to have an appeal letter made available to Council. 
The Council may agree with either the study section or the applicant. If the Council agrees with the applicant, it recommends appropriate actions to resolve the matter, which may include re-review of the application. If the Council concurs with the study section recommendation, the application will not be re-reviewed. The decision is final and may not be further appealed.
The Executive Secretary for the Council will communicate the Council recommendation concerning an appeal to the PD/PI, AOR, and NIH staff on a need to know basis.  If the appeal letter was received by the IC deadline, the PD/PI and AOR will receive a written explanation of the resolution no later than 10 working days after the Council meeting (  If the appeal letter was received after the IC deadline, the Executive Secretary will provide, no more than 30 calendar days after the date when the appeal letter was received, a written explanation of the IC’s plan for making the appeal available to Council. 
If the Council recommended that the application be re-reviewed, the original application will be re-reviewed without additional materials or modifications.  The application may be re-reviewed by the same or a different SRG, depending on the flaws in the original review process that led to the appeal.  In most cases, the re-review will entail re-assignment to a subsequent review round and delay in the final funding decision. The outcome of the re-review is final and cannot be appealed again.
Appeals of receipt and referral issues regarding applications not yet reviewed should be directed to the Referral Office, Center for Scientific Review.