We have probleme when $date >= 2002-10-20 <= 2002-10-31

You can try to do this :
------------EXAMPLE --------------
<?php

$date_depart 	= "2003-10-26";
// We add 7 days to $date_depart
$date_apres 	= calcul_date_ajoute_jour($date_depart,7);
// $date_apres is false ... ????
?>
------------END OF EXAMPLE --------------

// Add days to date
function calcul_date_ajoute_jour($date,$nbjour){ // Date au Format Am?ricain
	return date_plus($nbjour,1,$date);
}

function date_time($i) {
	$i = strtotime($i);
	//echo "$i = $i<br>";
	return mktime(
	date("H", $i),
	date("i", $i),
	date("s", $i),
	date("m", $i),
	date("d", $i),
	date("Y", $i));
}

function date_plus($e = 2, $o = 2,$d=1) {
	if ($d==1) $d=date("Y-m-d");
	
	$aujourdui = date_time($d);
	$apres = getdate(($aujourdui + (86400 * $e)));
	
	$mois=substr("0".$apres[mon],-2,2);
	$jour=substr("0".$apres[mday],-2,2);
	if($o == 2) return $mois . "-" . $jour;
	else return $apres[year] . "-" . $mois . "-" . $jour;
}