In order for your SMS messages to be successfully delivered, your contact's mobile numbers should be written in the correct international format.
Remove the first '0' or '+' of the mobile number and replace it with the relevant international code (e.g. 61 for Australia and 64 for New Zealand).
For example: 61 412 341 234
Incorrect formatting may result in undelivered messages, or a message being sent to an incorrect handset.