Keyword search in relational databases has been widely studied in recent years. Most of the previous studies focus on how to answer an instant keyword query. In this paper, we focus on how to find the top-k answers in relational databases for continuous keyword queries efficiently. As answering a keyword query involves a large number of join operations between relations, reevaluating the keyword query when the database is updated is rather expensive. We propose a method to compute a range for the future relevance score of query answers. For each keyword query, our method computes a state of the query evaluation process, which only contains a small amount of data and can be used to maintain top-k answers when the database is continually growing. The experimental results show that our method can be used to solve the problem of responding to continuous keyword searches for a relational database that is updated frequently. Key words: Relational databases, keyword search, continuous queries...