When a strong magnetic field is applied to a two-dimensional electron system, interactions between the electrons can cause fractional quantum Hall (FQH) effects^1,2. Bringing two two-dimensional conductors close to each other, a new set of correlated states can emerge due to interactions between electrons in the same and opposite layers^3,4,5,6. Here we report interlayer-correlated FQH states in a device consisting of two parallel graphene layers separated by a thin insulator. Current flow in one layer generates different quantized Hall signals in the two layers. This result is interpreted using composite fermion (CF) theory⁷ with different intralayer and interlayer Chern–Simons gauge-field couplings. We observe FQH states corresponding to integer values of CF Landau level (LL) filling in both layers, as well as ‘semiquantized’ states, where a full CF LL couples to a continuously varying partially filled CF LL. We also find a quantized state between two coupled half-filled CF LLs and attribute it to an interlayer CF exciton condensate.