Abstract Elements of the spin density matrix for W bosons in e + e −→ W + W −→ q q ̄ ′ℓν ℓ events are measured from data recorded by the OPAL detector at LEP. This information is used to calculate polarised differential cross-sections and to search for CP-violating effects. Results are presented for W bosons produced in e +e − Collisions with centre-of-mass energies between 183 GeV and 209 GeV. The average fraction of W bosons that are longitudinally polarised is found to be (23.9±2.1±1.1)% compared to a Standard Model prediction of (23.9±0.1)%. All results are consistent with CP conservation.