DECLARE @Table Table (id tinyint,kduedate date,asofdate date)
INSERT INTO @Table
VALUES
(1,'1900-01-01','2/12/2011'),
(1,'2012-01-02', '2/13/2011'),
(1,'1900-01-01', '2/12/2011'),
(2,'1900-01-01', '2/13/2011'),
(2,'1900-01-01', '2/14/2011'),
(2,'1900-01-01', '2/15/2011'),
(2,'2012-01-25', '2/16/2011')


SELECT DISTINCT id,
       COALESCE(tgt.newkduedate,t1.kduedate) AS newkduedate
FROM   @TABLE T1
       OUTER APPLY
(
    SELECT MIN(asofdate) AS newkduedate
    FROM   @Table t2
    WHERE  t1.id = t2.id
           AND t2.kduedate <> '19000101'
           AND t2.asofdate > t1.asofdate

) tgt
WHERE  t1.kduedate = '19000101'