After providing informed consent/assent, pediatric participants with Phelan-McDermid syndrome who participated in previous studies (NEU-2591-PMS-301 and NEU-2591-PMS-001) will undergo assessments for eligibility, baseline characteristics and symptom severity. Once eligibility is confirmed, participants will receive orally administered NNZ-2591 during the 52-week Treatment Period. A 2-week safety follow-up period will occur immediately after the completion of the Treatment Period.