We study a class of two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent and both players are budget-constrained. We extend the results for all-pay auctions with complete information, and show that in our class of all-pay auctions with asymmetric information, su¢ ciently high (but still binding) bid caps do not change the players’expected total e¤ort compared to the benchmark auction without any bid cap. Furthermore, we show that there are bid caps that increase the players’expected total e¤ort compared to the benchmark. Finally, we demonstrate that there are bid caps which may have an unanticipated e¤ect on the players’expected payo¤s –one player’s information advantage may turn into a disadvantage as far as his equilibrium payo¤ is concerned.