It depends on the
GNU/Linux distribution in question, and whether relevant packages for 32-bit compatibility have been installed. The relevant feature is usually called "
multilib". It also depends on support in the Linux kernel; it is possible to disable support for 32-bit binaries when the Linux kernel is compiled. The popular
Ubuntu distributions both support 32-bit compatibility, and several distributions that previously did not have it have added it (for example,
The above, of course, relates to running 32-bit programs on top of a 64-bit kernel and 64-bit capable CPU. Linux cannot run 64-bit applications on a 32-bit kernel, even if the CPU is 64-bit capable. If the CPU is not 64-bit capable, then you obviously won't get 64-bit applications to run without emulation.