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 derive from each other under certain general hypotheses such as uniform lower compactness property and locally uniform convergence of ƒα to ƒ. The result is applied to obtain some general lower semicontinuity theorems on multiple integrals with quasiconvex integrand ƒ, while ƒα are not required to be quasiconvex.