Yes, that is normal.
This is correspondence chess. Do not expect a game to be started and completed in a few hours. How often an opponent is required to make a move is determined by the "time out" setting selected when the game was initiated, and is measured in days.
Remember that members of this site form an international community and therefore log on and off of the site at all hours of the day and night, from around the world.
Some of us are here several times each day, others may only be here once a day, and some only two or three times in a week. It depends on many things, including other activities such as work, school, computer access, etc.
If you are looking for a quick game, go to the bottom of this page and click the 'uChess' link. At that site you can play live chess. The uChess site is still in it's early stages, and is being created by the same people who have put this site together.
Welcome to our little corner of the world!