unusual rate of unsolicited mail originating from your IP address

We got bounce message from 118.69.183.136. But why does it bounce to both [email protected] and [email protected]? Did they both send an email, which could not be delivered? Unlikely.

It isn't bouncing to the two addresses, it's bouncing it to postmaster telling you that delivery to those two addresses failed.

Then google replies with "421-4.7.0 [16.19.64.110 15] Our system has detected an unusual rate of unsolicited mail originating from your IP address. To protect our users from spam, mail sent from your IP address has been temporarily rate limited. Please visit http://www.google.com/mail/help/bulk_mail.html to review our Bulk Email Senders Guidelines." What is this supposed to mean?

It means you have been rate limited. You should go to the URL stated for more information. What part of that is unclear?

I doubt they send a lot of emails. Would you suggest a way to count them?

You're barking up the wrong tree. The message clearly states that your IP address is sending too many emails. This has nothing to do whom the messages are to or from, it's simply the number of messages from that exact IP address (your server) that are being sent to google. This includes your messages that are being generated to postmaster due to bounces/failures that are being forwarded to your gmail account.

You should realize you have a catch-22 here that if Google is limiting the amount of messages from your system to theirs and you have your errors (bounces, warnings) going to google as well..

In the end, the bounce messages get delivered. I'm running debian 6. Could you explain me what's going on and what am I to do?

You've sent enough messages from your IP to gmail servers and Google has temporarily (as it clearly says in the logs) rate limited. Those messages are generating errors (warnings) that they could not be immediately delivered. You then have those messages being forwarded to yet another gmail address which is creating even more attempts to send email through google's servers from your IP which is likely making the problem worse.

Once their temporary rate limiting has been lifted then your messages would go through as expected.

and what am I to do?
  1. You should follow the guidelines that Google already gave you in the error message.
  2. You should stop forwarding postmaster mail to google to keep the number of messages from your system to them down.

If those fail, you should consider paying Google to host the domain properly and/or stop forwarding messages to gmail accounts.