328 hoses from airbox

Changing belts (cam, WP, alt) and in removing the airbox I noticed the two hoses that attach to the airbox were very brittle though not cracked/leaking. So I figured I'd replace them. THEN I got to wondering, what do these hoses do? I assume they are associated with emissions. I tried to find a diagram, like Ricambi used to have on their site until they were forced to remove them but I didn't have any luck.

 

I should have been more clear - The two hoses I'm referring to are the two hoses that attach to the underside of the airbox. They run from the airbox underneath the intake manifold to the other side of the engine compartment.

Mike32 - thanks for the Eurospares suggestion - I found the hoses on their diagram and they are, indeed, part of the air injection emissions system. Trying to figure out if I need them since I removed the Cat some years ago after my Slow down light system went out of service. Since there are no emission checks here I was thinking of just blocking the relevant fittings.