The reactions γγ→π+π−π+π− and γγ→π+π0π−π0 are studied with the L3 detector at LEP in a data sample collected at centre-of-mass energies from 161 GeV to 209 GeV with a total integrated luminosity of 698 pb−1. A spin-parity-helicity analysis of the ρ0ρ0ρ0ρ0 and ρ+ρ− systems for two-photon centre-of-mass energies between 1 and 3 GeV shows the dominance of the spin-parity state 2+2+ with helicity 2. The contribution of 0+ and 0− spin-parity states is also observed, whereas contributions of 2− states and of a state with spin-parity 2+2+ and zero helicity are found to be negligible.