In this paper, we study the optimization of linear recursive queries using wavefront methods. The following results are obtained.(i) In spite of seemingly reasonable approach of the wavefront methods, certain linear recursive queries are not processed efficiently or correctly.(ii) A characterization of the expressions generated by linear recursive rules is given. Properties of the expressions will be useful for efficient processing of linear recursive queries.(iii) Conditions for efficient processing of linear recursive rules using wavefront methods with the properties given in (ii) are provided.