I'd heard there was a point in the late twentieth century when the Lubavitcher Rebbe (R' Menachem Mendel Schneurson) would give an address, which would be relayed to the Satmar Rebbe (R' Yoel Teitelbaum), who replied to it in one of his addresses; this continued for quite some time, until one of the rebbes had a stroke.
From what I understand, this was actually some form of a debate between the two (very different) Hassidic movements.
Can anyone provide more information about this, please?