  We study structure formation in K-mouflage cosmology whose main feature is
the absence of screening effect on quasilinear scales. We show that the growth
of structure at the linear level is affected by both a new time dependent
Newton constant and a friction term which depend on the background evolution.
These combine with the modified background evolution to change the growth rate
by up to ten percent since $z\sim 2$. At the one loop level, we find that the
nonlinearities of the K-mouflage models are mostly due to the matter dynamics
and that the scalar perturbations can be treated at tree level. We also study
the spherical collapse in K-mouflage models and show that the critical density
contrast deviates from its $\Lambda$-CDM value and that, as a result, the halo
mass function is modified for large masses by an order one factor. Finally we
consider the deviation of the matter spectrum from $\Lambda$-CDM on nonlinear
scales where a halo model is utilized. We find that the discrepancy peaks
around $1\ h{\rm Mpc}^{-1}$ with a relative difference which can reach fifty
percent. Importantly, these features are still true at larger redshifts,
contrary to models of the chameleon-$f(R)$ and Galileon types.
