Background: In the EXIST-1 trial, initiated on Aug 10, 2009, more than 35% of patients with subependymal giant cell astrocytoma (SEGA) associated with tuberous sclerosis complex had at least 50% reduction in SEGA volume after 9.6 months of treatment with everolimus. In this Article, we report interim data (up to Jan 11, 2013) to support longer-term tolerability and efficacy of everolimus from the continuing 4-year extension phase of EXIST-1. Methods: We assessed data from a prospective, open-label extension of a multicentre, phase 3, randomised, double-blind, placebo-controlled study in patients with tuberous sclerosis complex who had SEGA that was growing and needed treatment. In this extension study, we included all patients who had been assigned everolimus during the double-blind, randomised phase of the trial and those patients who crossed over from the placebo group to receive everolimus during the randomised phase or at the start of the extension phase. All patients received oral everolimus at a starting dose of 4.5 mg/m2 per day. Everolimus dose was subsequently adjusted subject to tolerability to attain blood trough concentrations of 5-15 ng/mL. An independent central radiology review team assessed SEGA response (at least a 50% reduction from baseline in total volume of all target SEGAs; the primary endpoint) by MRI at 12, 24, and 48 weeks, then every year thereafter in all patients who received at least one dose of everolimus. This study was registered with ClinicalTrials.gov, number NCT00789828. Findings: Of the original 117 randomly assigned patients, 111 were given everolimus between Aug 20, 2009, and Jan 11, 2013 (date of data cutoff); we included these patients in our longer-term analysis. Median duration of everolimus exposure was 29.3 months (IQR 19.4-33.8). Median follow-up was 28.3 months (IQR 19.3-33.0). 54 (49%) patients had a response of 50% or greater reduction in SEGA volume (95% CI 39.0-58.3), and duration of response was between 2.1 and 31.1 months (median not reached). SEGA volume was reduced by 50% or more in 39 (37%) of 105 patients at 24 weeks, 48 (46%) of 104 patients at 48 weeks, 36 (47%) of 76 patients at 96 weeks, and 11 (38%) of 29 patients at 144 weeks. Stomatitis (48 [43%] patients) and mouth ulceration (33 [30%] patients) were the most frequent treatment-related adverse events; infections were the most commonly reported treatment-related serious adverse event, occurring in 15 (14%) patients. 35 (32%) patients reported treatment-related grade 3 or 4 adverse events, the most common of which were stomatitis (nine [8%]) and pneumonia (nine [8%]). 18 (16%) patients had treatment-related serious adverse events. Six (5%) patients withdrew because of adverse events. Interpretation: These results support the longer-term use of everolimus in patients who have few treatment options and who need continued treatment for tuberous sclerosis complex and its varied manifestations. Reduction or stabilisation of tumour volume with everolimus will hopefully provide long-term clinical benefit in patients with SEGA.