The trial will use a double blind placebo-controlled parallel-group flexible-dose forced titration design in which 100 subjects with FXS, age 32 months to 6 years of age will enter a 12-month blinded treatment phase during which they are randomized 1:1 to AFQ056 or placebo followed by an 8-month (open label) extension phase in which all participants will be treated with active drug. The flexible dose design will mimic practice, take into account differential responsiveness and the known inter-child variability in drug levels with AFQ056, and allow use of maximum tolerated dose (MTD) which is likely to be most effective.