On weak bases in functional spaces

For a strictly webbed Montel space $E$ with complete separable $E'_\beta$ (strong dual of $E$), we show that a weak bases in $E$ is Schauder basis with equicontinuons coefficientive functionals. This result is applied to bases in spaces of holomorphic functions. In particular, from it the absolutenes of all bases in some classes of nonmetrizable nuclear functional spaces follows.