A fibred category consists of a functor $p:\mathbf N\longrightarrow \mathbf M$ between categories $\mathbf N$ and $\mathbf M$ such that
 objects of $\mathbf N$ may be "pulled back along any arrow of $\mathbf M$". Given a fibred category $p:\mathbf N\longrightarrow \mathbf M$ 
 and a model structure on the "base category" $\mathbf M$, we show that there exists a lifting of the model structure on $\mathbf M$ to a 
 model structure on $\mathbf N$. We will refer to such a system as a "fibred model category" and give several examples of such structures.
 We show that, under certain conditions, right homotopies of maps in the base category $\mathbf M$ may  be lifted to right homotopic maps 
 in the fibred category. Further, we show that these lifted model structures are well behaved with respect to Quillen adjunctions and Quillen 
 equivalences. Finally, we show that if $\mathbf N$ and $\mathbf M$ carry compatible closed monoidal structures and the functor $p$ commutes 
 with colimits, then a Quillen pair on $\mathbf M$ lifts to a Quillen pair on $\mathbf N$.