It depends on the format of the date:
01/11/10
01/02/2010
2010/01/02
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2002
Millennia usually end in zero, so they can't be palindromes. The next palindromic year will be 2112.
2002 was a palindromic year if we have the format day/mo/yr 10/02/2001
The next palindromic number after 1991 is 2002. A palindromic number reads the same forwards and backwards. In this case, 2002 reads the same whether you read it left to right or right to left.
The next palindromic years are going to be 2112 and 2222. There is a 100 year difference between the two.