  In this paper the concept of compatible weak factorization systems in general
categories is introduced as a counterpart of compatible complete cotorsion
pairs in abelian categories. We describe a method to construct model structures
on general categories via two compatible weak factorization systems satisfying
certain conditions, and hence generalize a very useful result by Gillespie for
abelian model structures. As particular examples, we show that weak
factorizations systems associated to some classical model structures (for
example, the Kan-Quillen model structure on $\mathsf{sSet}$) satisfy these
conditions.
