The standard MinGW libraries will probably be incomplete, causing
'undefined symbol' errors. So get the latest
mingw-w32api RPM
and use alien to either convert it to a .tar.gz file
from which to extract just the relevant files, or to convert it
to a Debian package that you will install.
This includes Fedora Core, Red Hat Enterprise Linux, Mandrake,
most probably SuSE Linux too, etc. But this list isn't exhaustive;
the following steps should probably work on any rpm based system.
Download and install the latest rpm's from
MinGW RPM packages.
Alternatively you can follow the instructions on that page and
build your own packages from the source rpm's listed there as well.
The *BSD systems have in their ports collection a port for the
MinGW cross-compiling environment. Please see the documentation
of your system about how to build and install a port.