  We consider $C$-compact orthogonally additive operators in vector lattices.
After providing some examples of $C$-compact orthogonally additive operators on
a vector lattice with values in a Banach space we show that the set of those
operators is a projection band in the Dedekind complete vector lattice of all
regular orthogonally additive operators. In second part of the article we
introduce a new class of vector lattices, called $C$-complete, and show that
any laterally-to-norm continuous $C$-compact orthogonally additive operator
from a $C$-complete vector lattice to a Banach space is narrow, which
generalizes a result of Pliev and Popov.
