You can use sed for this. For example:
$ sed -n '/Feb 23 13:55/,/Feb 23 14:00/p' /var/log/mail.log
Feb 23 13:55:01 messagerie postfix/smtpd[20964]: connect from localhost[127.0.0.1]
Feb 23 13:55:01 messagerie postfix/smtpd[20964]: lost connection after CONNECT from localhost[127.0.0.1]
Feb 23 13:55:01 messagerie postfix/smtpd[20964]: disconnect from localhost[127.0.0.1]
Feb 23 13:55:01 messagerie pop3d: Connection, ip=[::ffff:127.0.0.1]
...
How it works
The -n switch tells sed to not output each line of the file it reads (default behaviour).
The last p after the regular expressions tells it to print lines that match the preceding expression.
The expression '/pattern1/,/pattern2/' will print everything that is between first pattern and second pattern. In this case it will print every line it finds between the string Feb 23 13:55 and the string Feb 23 14:00.
More info here. (archived)
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