The authors consider the retarded Liénard equation
where is a nonnegative constant, , and are continuous functions on , and is a continuous function on . They obtain some new sufficient conditions, as well as some new necessary and sufficient conditions for all solutions and their derivatives to be bounded avoiding the following traditional conditions:
(H1) for all or when is large;
(H2) there exists a constant such that
(H3) for all or when is large. Two illustrative examples are also included.