We present measurements of the lifetimes and polarization amplitudes for B0s→J/ψϕ and B0d→J/ψK*0 decays. Lifetimes of the heavy and light mass eigenstates in the B0s system are separately measured for the first time by determining the relative contributions of amplitudes with definite CP as a function of the decay time. Using 203±15 B0s decays we obtain τL=(1.05+0.16−0.13±0.02)  ps and τH=(2.07+0.58−0.46±0.03)  ps. Expressed in terms of the difference ΔΓs and average Γs, of the decay rates of the two eigenstates, the results are ΔΓs/Γs=(65+25−33±1)% and ΔΓs=(0.47+0.19−0.24±0.01)   ps−1