Today this fast is considered part of the Great Fast, a preparation period in which we enter gradually into the asceticism of the Fast. It originated, however, in the Oriental Orthodox (non-Chalcedonian) Churches and was separate from the Great Fast. It was called the fast of Nineveh, and was observed three weeks before the Great fast, in what is now the Week after the Sunday of the Publican and the Pharisee. The Byzantine Church would not observe it at the same time as those Churches in which it was not in communion and moved it to the Week before the Great Fast.
From the Typicon (guidebook for the liturgies of the church)
Sunday, February 20 –
