I apologize for being not clear enough. The ASPxTextBox control has no built-in feature similar to the AutoCompleteExtender. However, you can use the ASPxComboBox with the enabled EnableIncrementalFiltering option (see ASPxComboBox Features (Filtering)). Please also check the ASPxComboBox - Populating on the Fly demo module. Let me know whether this makes sense.
See also: Autocomplete bound field.
