Well you need a while loop indeed (or rather, a while loop is the obvious way to do it). Just write while instead of if, and do think about changing the value of $initial_number (maybe change its name) to give it the value of $new_number at the end of the loop. There's no else with a while loop.

And since this is very basic perl, you may want to read perlintro

use warnings;
use strict;

print "Please give me a number:\n";
my $initial_number = <STDIN>;
chomp $initial_number;

while (1) {
    print "Please continue with a new number:";
    my $new_number = <STDIN>;
    chomp $new_number;
    if ($new_number < $initial_number) {
        print "You specified a number which is smaller than the previo
+us. The program will now exit\n";
        exit;
    }
    $initial_number = $new_number;
}
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And the last statement will exit (I believe ...) from that loop. The next statement will branch back to the start of the loop again. As long as there is eventually some way out of the loop, an infinite loop is sometimes perfect perfect perfect perfect perfect perfect perfect perfect perfect perfect.

Ah, thanks to all of you for your suggestions!

print "Enter num1\n";
my $num1 = <STDIN>;
chomp ($num1);

print "Enter num2\n";
my $num2 = <STDIN>;
chomp($num2);

while($num2 > $num1)
{
    print "Enter num again\n";
    my $num = <STDIN>;
    chomp($num);

    $num1 = $num2;
    $num2 = $num;
}

print "Num2 is smaller than Num1\n";
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