  Weaving frames are powerful tools in wireless sensor networks and
pre-processing signals. In this paper, we introduce the concept of weaving for
g-frames in Hilbert spaces. We first give some properties of weaving g-frames
and present two necessary conditions in terms of frame bounds for weaving
g-frames. Then we study the properties of weakly woven g-frames and give a
sufficient condition for weaving g-frames. It is shown that weakly woven is
equivalent to woven. Two sufficient conditions for weaving g-Riesz bases are
given. And a weaving equivalent of an unconditional g-basis for weaving g-Riesz
bases is considered. Finally, we present Paley-Wiener-type perturbation results
for weaving g-frames.
