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There are two forms of cloud POS software: web-based and app-based. 

A web-based POS relies entirely on the cloud, and is accessed through a web browser. Nothing is local to your operating system, meaning that everything—your inventory, sales data, employee timekeeping, customer information, etc. is tied up in a system that needs to be in constant communication with the servers hosting your data through an Internet connection.

This is Possible via HTML5 Caching (or Offline Caching), which basically creates a mirroring copy of your data every time you change something, one copy is sent to the external servers, the other is saved within your browser’s cache. 

Credit card transactions are not possible in the offline mode as making credit card payment requires accessing the customer database, for which eventually an active internet connection is required. The merchant might advice you that it will accept, however the result will be a declined transaction.