3.4 Can I use Debian packages (".deb" files) on my Red Hat/Slackware/... Linux system? Can I use Red Hat packages (".rpm" files) on my Debian GNU/Linux system?

Different Linux distributions use different package formats and different package management programs.

You probably can:

A program to unpack a Debian package onto a Linux host that is been built from a `foreign' distribution is available, and will generally work, in the sense that files will be unpacked. The converse is probably also true, that is, a program to unpack a Red Hat or Slackware package on a host that is based on Debian GNU/Linux will probably succeed in unpacking the package and placing most files in their intended directories. This is largely a consequence of the existence (and broad adherence to) the Linux Filesystem Hierarchy Standard. The Alien package is used to convert between different package formats.

You probably do not want to:

Most package managers write administrative files when they are used to unpack an archive. These administrative files are generally not standardized. Therefore, the effect of unpacking a Debian package on a `foreign' host will have unpredictable (certainly not useful) effects on the package manager on that system. Likewise, utilities from other distributions might succeed in unpacking their archives on Debian systems, but will probably cause the Debian package management system to fail when the time comes to upgrade or remove some packages, or even simply to report exactly what packages are present on a system.

A better way:

The Linux File System Standard (and therefore Debian GNU/Linux) requires that subdirectories under /usr/local/ be entirely under the user's discretion. Therefore, users can unpack `foreign' packages into this directory, and then manage their configuration, upgrade and removal individually.