  Answering a question of Garbuli\'nska-W\c{e}grzyn and Kubi\'s, we prove that
Gurarii operators form a dense $G_\delta$-set in the space $\mathcal B(\mathbb
G)$ of all nonexpansive operators on the Gurarii space $\mathbb G$, endowed
with the strong operator topology. This implies that the set of universal
operators on $\mathbb G$ form a residual set in $\mathcal B(\mathbb G)$.
