on credit
Bought owing some or all of something's cost in the future, either in full or in instalments, instead of paying that money upfront. We desperately needed a new car but our savings were pretty depleted, so we had to buy it on credit. You need to stop buying things on credit, or you're going to be in debt for the rest of your life.
on credit
using credit; buying something using credit. I tried to buy a new suit on credit, but I was refused. The Smiths buy everything on credit and are very much in debt.