Some people owe debts to me, and it is time for me to give Zakaah. Is it valid to relieve them of repaying these debts instead of paying Zakaah?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Removal of debt may not be taken as a substitute for payment of Zakah. The reason for this probably lies in the fact that intention is a condition when paying Zakah to its due recipients. You gave this money as a debt, not as Zakah. Moreover, Zakah involves giving and taking, as deduced from the verse in which Allaah The Exalted Says (what means): {Take, [O, Muhammad], from their wealth a charity by which you purify them and cause them increase}[Quran 9:103]

Such is a mere removal of debt, not involving any form of giving by you or taking by them. Furthermore, this procedure is intended for you to save money. If you want to drop the debt, or part of it, to make things easy for them, this act is commendable and rewardable by Allaah The Almighty, Who Says (what means): {And if someone is in hardship, then [let there be] postponement until [a time of] ease. But if you give [from your right as] charity, then it is better for you, if you only knew}[Quran 2:280]

Yet, you are not permitted to remove the debt as a substitute for paying Zakah, in which case you will still be required to pay Zakah to them, if they deserve it, or to other people regarded as due recipients of Zakah.