Epileptic encephalopathies are a devastating group of severe childhood epilepsy disorders for which the cause is often unknown1. Here we report a screen for de novo mutations in patients with two classical epileptic encephalopathies: infantile spasms (n = 149) and Lennox–Gastaut syndrome (n = 115). We sequenced the exomes of 264 probands, and their parents, and confirmed 329 de novo mutations. A likelihood analysis showed a significant excess of de novo mutations in the ∼4,000 genes that are the most intolerant to functional genetic variation in the human population (P = 2.9 × 10−3). Among these are GABRB3, with de novo mutations in four patients, and ALG13, with the same de novo mutation in two patients; both genes show clear statistical evidence of association with epileptic encephalopathy. Given the relevant site-specific mutation rates, the probabilities of these outcomes occurring by chance are P = 4.1 × 10−10 and P = 7.8 × 10−12, respectively. Other genes with de novo mutations in this cohort include CACNA1A, CHD2, FLNA, GABRA1, GRIN1, GRIN2B, HNRNPU, IQSEC2, MTOR and NEDD4L. Finally, we show that the de novo mutations observed are enriched in specific gene sets including genes regulated by the fragile X protein (P < 10−8), as has been reported previously for autism spectrum disorders2.