perhaps you should be using the s/// operator instead...

#!/usr/bin/perl -wT
use strict;

my $line = "I like 'balls' and 'rings', do you like 'rings' and 'balls
+'?";
print "Before = $line\n";
$line =~ s/(balls|rings)//g;
print "After  = $line\n";

=output
Before = I like 'balls' and 'rings', do you like 'rings' and 'balls'?
After  = I like '' and '', do you like '' and ''?
[download]

Update: Apparently the question is an AND one, not an OR one (which is what I provided an answer to). In general, I think mutiple regexes are best for this sort of thing. i.e. if (/balls/ && /rings/) { } there are tricky ways of doing this in one regex, but they tend to be slower, and less readable.

-Blake