In November last year, I talked about the 2-out-of-3 property for ω-weak equivalences between weak ω-categories (in the sense of Batanin-Leinster). These ω-weak equivalences are the strict ω-functors which are essentially surjective at every dimension. In this talk, I define weak ω-weak equivalences as weak ω-functors (in the sense of Garner) which are essentially surjective in a suitable sense. I show a few results about them, including the 2-out-of-3 property and their characterisation in terms of the underlying globular map of a weak ω-functor. (Joint work with Keisuke Hoshino and Yuki Maehara.)