Can I have VALID L1 and H1B Both at the Same Time?

If we would have L1 and H1 B both ( L1 from Company side and H 1B our own side) then Is it mandatory to work upon H1 B Or we can still work on L1 after october 2013? In other words can I have both L1 and H1B at the same time while still working on L1 ?

After Oct 1, 2013 you will be pushed to H1B automatically.

Please read my post and vote for the petition: http://redbus2us.com/qa/9659/please-vote-for-this-petition

It depends on your I-94. If you have entered US with L1 and your status remains L1 until you change it or re-enter with another visa. If your I-94 remains L1, then you cannot work for H1 employer. If you have got H1 by the means of COS from L1 with some effective date (in which your I94 changes to H1 from L1), then you cannot continue in L1 from the effective date.