An A600 can also take a PCMCIA network card. I have mine running with AmiTCP 4.0 (demo version) using Cloanto Amiga Explorer and NCFTP to transfer files. I get about 60kB/s but it beats a serial connection. If I can find my old AmiTCP keyfile I'll try AmiTCP 4.3 and see if it's any faster.
