strange mail connections

We have the strangest thing happening in our network.

The one incoming mail server is receiving zillions of full TCP connections 
from IP addresses that should not normally connect directly to the email 
server. The connection is past to the upper session layers as SMTP 
connections. The connections are established but "no message data" is 
present or sent in the packet.

The volume/amount of these connections is causing degradation of the server 
in that it fills the smtp connection table thus not allowing new 
connections.

Is there a new/old attack that could be doing this?

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