I tried to open dxlive.com, livedechat.tv, kanjukulive.com but they seem to require to register or use japanese language on pictures, so I can't translate it.

A also tried hxxp://www.sakuralive.com/japanese-webcam-girls.html
The free previews use RTMP protocol, so there should be no problem capturing with Replay Media Catcher 4 in the RTMP recording mode. You can also try to capture such streams with CooJah (without Blader).

Most probably private chats use RTMPE protocol, so try to capture them with freeware CooJah (without Blader) or with rtmpsuck.

RTMP recorders and RTMPE recorders which download RTMP and RTMPE streams will probably not work, but you can try them as well.

And of course you can use screen video capture software.