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Hello,

When I use of the following expressions to finish an e-mail or a letter, should I thank after it or it is not necessary?

1. I am looking forward to hearing from you / I look forward for a comment from you.

Regards,

Ruca.

or

2. I am looking forward to hearing from you / I look forward for a comment from you.

Thank you.

Regards,

Ruca.

Many thanks,

Rui.
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Greetings, Rui,

Saying 'thank you' is not usual in this closing part of a letter, so #1 is preferable. Also, I would definitely say: I look forward to receiving your comment.

Respectfully, Gleb Chebrikoff
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For e-mails at work, I routinely end mine with

Thanks,
Barb
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Comments  
It depends on the rest of the context-- are you thanking the recipient for something specific? However, the way I usually wrap up this sort of letter is:

Thank you very much for considering my application/submission/whatever, and I am looking forward to your positive response/comments/favorable decision/whatever.

Sincerely yours, ('Regards' is too casual)
 Andriy Lapin's reply was promoted to an answer.
 BarbaraPA's reply was promoted to an answer.
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Along what others already have pointed out, here is a side note. "Look forward to" is a fixed verb phrase. So "for" would be an incorrect usage, and for a formal correspondence, " I look forward for a comment from you " would sound a bit odd; if the intended meaning was: " I am looking forward to your reply ".
Thank you all for your comments.

Rui.