When I came in, the consoles of both machines were full of messages
like 'Can't get a page' and ARP complaining about being unable to
allocate memory.
After rebooting I examined the logs; nothing except one complaint from
ftpd that it couldn't allocate any memory, followed by nothing until I
rebooted. It seems to be the case that they completely ran out of
free memory. Both had in excess of 50Mb of swap and weren't running
anything big enough to account for this.
-Matt