- Study participant is male or female and must be at least 18 years of age at the time of signing the informed consent form (ICF). - Study participant must have a documented diagnosis of gMG, based on study participant's history and supported by previous evaluations. - Study participant is currently participating in ZLP (zilucoplan) study RA101495-02.302 (NCT04225871) or is administering commercial ZLP on a stable dosing regimen for at least 1 month prior to Screening. - Study participants on commercial ZLP need to receive ZLP per the approved local labeling. - Study participant is considered reliable and capable of adhering to the study protocol (eg, able to understand and complete questionnaires and able to adhere to the visit schedule) according to the judgement of the Investigator. - Study participant is willing and capable of self-administering ZLP using the zilucoplan-auto-injector (ZLP AI) according to the instructions for use (IFU), ie, does not have any visual, physical, or other disability or impairment that interferes with his/her capacity to self-administer; if the participant has a caregiver, he/she may assist the participant with the injection. - Vaccination with a quadrivalent meningococcal vaccine and, where available, meningococcal serotype B vaccine at least 14 days prior to investigational medicinal product (IMP) administration, if not vaccinated within 3 years prior to the start of treatment. Booster vaccination(s) should also be administered as clinically indicated, according to the local standard of care, for participants who have been previously vaccinated against Neisseria meningitidis. - Female participants of childbearing potential must have a negative urine pregnancy test prior to the first dose of study drug. - Male and/or female study participants a. A male participant must agree to use contraception during the Treatment Period and for 40 days after the last dose of study medication, and refrain from donating sperm during this period. b. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least 1 of the following conditions applies: - Not a woman of childbearing potential (WOCBP) OR A WOCBP who agrees to follow the contraceptive guidance the Treatment Period and for 40 days after the last dose of study medication. - Capable of giving signed informed which includes compliance with the requirements and restrictions listed in the ICF and in this protocol.