  Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames,
which was motivated by a problem regarding distributed signal processing. In
this present article, we introduce the atomic $g$-system and we generalize some
of the known results in continuous $L$-frames, weaving continuous and weaving
continuous $ g$-frames, also we study weaving continuous $ L$-$g$-frames in
Hilbert spaces.
  Moreover, we study the behaviour continuous $ L$-$g$-frames under some
perturbations, and we show that approximate $L$-duals are stable under small
perturbation and that it is possible to remove some elements of a woven
continuous $ L$-$g$-frame and still have a woven continuous $ L$-$g$-frame.
