You may join, switch or drop your current Medicare Prescription Drug plan during Medicare's Annual Enrollment Period (AEP). You may also make changes to your Medicare prescription drug coverage during a Special Enrollment Period (SEP), when certain non-routine events happen in your life. Enrollment in Medicare prescription drug coverage during the Annual Enrollment Period (AEP) takes place from October 15 through December 7. Some people are eligible to enroll during the Special Enrollment Period (SEP) if they meet one of several criteria.