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First and foremost, PayPal recommends using DNS to determine the IP address of our servers. We change DNS often, and do not notify ahead of time. If you choose not to use DNS, you should know that at all times except during scheduled maintenance, at least one of the IPs listed below for each system will be live and serving traffic. But not all of them will be, and it is the responsibility of the end user's application to know how to cycle through all the addresses until it finds one that is working.
In Q1 2012 the IP addresses for PayPal API endpoints, svcs.paypal.com endpoint and ipnpb.paypal.com post back url will be expanded further. Please see the list of additional IP addresses at the bottom of this list, and you can read more about this upcoming change here
Subscribe to this FAQ if you would like to be notified when IPs are added or removed.

Current IPs:

------------api.paypal.com---------
66.211.168.91
66.211.168.123
173.0.88.66 (only as a backup site coming online in October 2011)
173.0.88.98 (only as a backup site coming online in October 2011)
173.0.84.66(only as a backup site coming online in November 2011)
173.0.84.98(only as a backup site coming online in November 2011)

(or) IP ranges:

173.0.80.0/20
66.211.160.0/19
------------api-aa.paypal.com------------
66.211.168.92
66.211.168.124
173.0.88.67 (only as a backup site coming online in October 2011)
173.0.88.99 (only as a backup site coming online in October 2011)
173.0.84.99 (only as a backup site coming online in November 2011)
173.0.84.67 (only as a backup site coming online in November 2011)

(or) IP ranges:

173.0.80.0/20
66.211.160.0/19

------------api-3t.paypal.com------------
66.211.168.126
66.211.168.194
173.0.88.69 (only as a backup site coming online in October 2011)
173.0.88.101 (only as a backup site coming online in October 2011)
173.0.84.69(only as a backup site coming online in November 2011)
173.0.84.101(only as a backup site coming online in November 2011)