The regular expression works, but not in the way you intended it to. It would have been helpful if you had given the output you got and the output you expected, together with an indication of the differences, but in this case, it's easy :

# You get :
<TAG1> BALHBLAHBLAHBLAH <TAG2> ASDFASDFASDFASD <TAG3>

# You expect :
<TAG1> balhblahblahblah <TAG2> asdfasdfasdfasd <TAG3>
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What is happening is, that the .+ part does not stop matching after meeting the first closing angle bracket but goes on matching further. I show the difference below :

This behaviour of .* is called greedy. There is a lazy (non-greedy) version of .* that is written .*?, which does what you want :

#!/usr/bin/perl

$x="<tag1> balhblahblahblah <tag2> asdfasdfasdfasd <tag3>";
$x=~s/<(.+?)>/<\U$1\E>/;
print $x;
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perl -MHTTP::Daemon -MHTTP::Response -MLWP::Simple -e ' ;    # The  
$d = new HTTP::Daemon and fork and getprint $d->url and exit;#spider
($c = $d->accept())->get_request(); $c->send_response( new   #in the
HTTP::Response(200,$_,$_,qq(Just another Perl hacker\n))); ' #  web
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