Twitter alerts generally are the replies, or the direct messages that someone sent to you. And generally you get notified via mail when a DM arrives your way but replies have no alerts. But here is a new service that alerts you through SMS, for all the replies and DM you receive. And these are alerts sent together every hour.

This is Twe2 service. It is just launched and sends alerts to mobile phones, throughout the world. And this amazing service works perfectly when tested.
You just have to login to the site with twitter credentials, provide your mobile number, and then confirm the mobile with the confirmation code sent to your mobile, and you are set.
You would get a certain number of SMS alerts every hour that you have set.

And usually these type of services are available in U.S. and U.K. but this Twe2 service is available for many countries around the world, includes many Asian and American countries. This service also shows the sent tweet replies or direct messages that you are receiving from your followers or friends.

Here is a list of countries where the Twe2 service works in sending SMS alerts.