Attentive listening systems are designed to let people, especially senior people, keep talking to maintain communication ability and mental health. This paper addresses key components of an attentive listening system which encourages users to talk smoothly. First, we introduce continuous prediction of end-of-utterances and generation of backchannels, rather than generating backchannels after end-point detection of utterances. This improves subjective evaluations of backchannels. Second, we propose an effective statement response mechanism which detects focus words and responds in the form of a question or partial repeat. This can be applied to any statement. Moreover, a flexible turn-taking mechanism is designed which uses backchannels or fillers when the turn-switch is ambiguous. These techniques are integrated into a humanoid robot to conduct attentive listening. We test the feasibility of the system in a pilot experiment and show that it can produce coherent dialogues during conversation.