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Check this article.<br />
<a href="https://technet.microsoft.com/en-us/library/bb124911%28v=exchg.141%29.aspx" rel="ugc">https://technet.microsoft.com/en-us/library/bb124911%28v=exchg.141%29.aspx</a><br />
Also make sure you have completed the per-requisites mentioned in above article i.e., MX records in place for the additional domains.
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Check this article.
https://technet.microsoft.com/en-us/library/bb124911%28v=exchg.141%29.aspx [https://technet.microsoft.com/en-us/library/bb124911%28v=exchg.141%29.aspx]
Also make sure you have completed the per-requisites mentioned in above article i.e., MX records in place for the additional domains.

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In Exchange 2010 we have our main domain name and then we have two other domain names, so each user they have 3 possible email addresses they can use. &nbsp;We can receive from all three addresses internally. &nbsp;However we can only receive from external email addresses to the main email address. &nbsp;If I try to send an email address from like gmail I get the following error: &nbsp;554 5.7.1 Error: deny openrelay. &nbsp;Where would I need to add these other email addresses in Exchange?
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In Exchange 2010 we have our main domain name and then we have two other domain names, so each user they have 3 possible email addresses they can use.  We can receive from all three addresses internally.  However we can only receive from external email addresses to the main email address.  If I try to send an email address from like gmail I get the following error:  554 5.7.1 Error: deny openrelay.  Where would I need to add these other email addresses in Exchange?

Error 554 5.7.1 Error: deny openrelay

Exchange is the server side of a collaborative application product that is part of the Microsoft Server infrastructure. Exchange's major features include email, calendaring, contacts and tasks, support for mobile and web-based access to information, and support for data storage.