Networking troubles with multiple nics

[Eric Eelkema <eelk0004@umn.edu>]

Hi,

I have a 486 with three 3c509 cards set up as a router.  It
took some work to get the cards on different IRQs, but I
think I did that correctly, and all of them work individually.
The problem is, when I bring up both interfaces to the internal
network, the one I bring up first works, but the other doesn't.  
Has anyone had this problem before?  More importantly, what can
I do to fix it?

More info:
Router eth0 is dhcp, connected to the cable modem
       eth1 is 192.168.1.3
       eth2 is 192.168.1.4
Internal computer A has eth0 192.168.1.1 connected to 192.168.1.3
Internal computer B has eth0 192.168.1.2 connected to 192.168.1.4

A session at the router looks like:
# ifup eth1 eth2
eth1: Setting Rx mode to 0 addresses.
eth1: Setting Rx mode to 1 addresses.
eth2: Setting Rx mode to 0 addresses.
eth2: Setting Rx mode to 1 addresses.
# ping 192.168.1.1
[...] 0% packet loss
# ping 192.168.1.2
[...] 100% packet loss
# ifdown eth1 eth2
# ifup eth2 eth1
eth2: Setting Rx mode to 0 addresses.
eth2: Setting Rx mode to 1 addresses.
eth1: Setting Rx mode to 0 addresses.
eth1: Setting Rx mode to 1 addresses.
# ping 192.168.1.1
[...] 100% packet loss
# ping 192.168.1.2
[...] 0% packet loss

The state of the router's eth0 doesn't seem to make any difference
(and it works just fine).  Any pointers to what the problem could
be are much appreciated.  Thanks in advance.