Unfortunately they do not. I use to use my Debit MC to make online payments with many companies. The payment is credited to the account right away and it is quicker than internet banking to debit your bank account. Most other campanies accept my debit MC but Telus denies it every time during the approval portion of the payment. I submitted a question as a "new idea" quite some time ago. Telus did not change their policy on Debit MC payments and closed the idea.