Granting one more domains to access asp.net site

Hi,

We used to have only one domain in our company, now we have 2 domains. In order to grant these new domain users to the access the asp.net site, will  "Network Service" take care of both domains automatically? Or do I have to explicitly add the new domain to the setting? If that is the case, please advice on how that can be done.

Thanks in advance. Your help would be greatly appreciated!