Well, on a sufficiently Unix-inspired system you could start the program in the background using the system's syntax for that. You could also fork() and exec(), then continue processing in the parent process.

my $kid_pid = fork() or die "Cannot fork!\n";
exec( '/bin/ls' ) unless $kid_pid;
my $keep_going = 1;
while ( $keep_going ) {
   ...
}
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See the fork info in perlfunc for more information.