Name resolution on Debian/Windows network

[Jeffrey Barish <jeffbarish@starband.net>]

I have 3 computers on my home network.  The Windows machines are
connected to each other using ICS.  I can ping one Windows machine from
another Windows machine simply by naming the destination:

ping windowsB

from machine windowsA will elicit a response.  I can also ping my Linux
machine from a Windows machine by name:

ping linuxA

from machine windowsA will elicit a response.  However, I cannot ping
one of the Windows machines by name from the Linux machine, only by IP
number.  I get the message 'unknown host windowsA.'  I am using DHCP to
assign IP numbers on the network, so it is important that I be able to
reach machines by name as the IP numbers change.  I'm not even sure
where to start looking to resolve this problem, so any guidance would
be appreciated.
-- 
Jeffrey Barish