Does the German direct-debit system work with online payments?

We have the same direct-debit system in Norway, called BankAxept, which is managed by a consortium of banks; banks typically issue cards with both Visa and BankAxept built in. However, BankAxept does not work with online payments.

A new system, BankAxess, has been launched for online payments, but it has not been widely implemented yet, so most online stores offer payment by Visa/Mastercard. Visa/MC's fees are somewhat exuberant, so most stores also offer COD and payment by wire transfer as alternative options.