Lower semicontinuity of multiple integrals ∫Ωƒ(x,uα,Pα)dµ and ∫Ωƒα(x,uα,Pα)dµ are studied. It is proved that the two can derivefrom each other under certain general hypotheses such as uniform lowercompactness property and locally uniform convergence of ƒα to ƒ. Theresult is applied to obtain some general lower semicontinuity theoremson multiple integrals with quasiconvex integrand ƒ, while ƒα are notrequired to be quasiconvex.