If you want to login in two different Gmail accounts or any other two/or more email accounts in same browser like hotmail, yahoo, rediff etc. you have to first logout first one otherwise same account will open in new window or new tab.
There is one easy solution open two Gmail or any other email account in two different browser like open one account in Internet Explorer and second one in Firefox or Chrome browser. But if you have only one browser or ease of use want to open two account in same browser you can do this by private browsing. In private browsing browser will not save cookies or any browsing history.
To open two account first open one account in normal mode in Internet explorer, Chrome, Firefox there after open second account using private browsing window. To open private window in Internet explorer click on tools than click on Inprivate browsing, for Mozilla firefox click on file than click new private window, for Google Chrome click on option menu than click ” New incognito window” (keyboard shortcut is ctrl+shift+N).