A .my third level domain name (3LD) is the common domain name extension that you see (eg. .com.my, .net.my, .org.my, etc). It is quite seldom that you find a website with a .my second level domain name (2LD) of .my. Two examples that I can find is Jaring.my and UKM.my.
Jaring.my was registered in the year 1992 while UKM.my in the year 1996. I guess they must have stopped selling the 2LD after that but it seems like the domain name is back on sale again.
There will be a priority period starting 1st November 2007 at 9am until 31st December 2007 at 5pm. During this period, all existing 3LD owners can apply for their equivalent 2LDs. For example, if you own the domain domain.com.my, you can apply for the domain.my domain.
Problem arises when two different 3LD owners with the same domain prefix wants the same 2LD (eg. domain.com.my and domain.net.my). In such a case, whoever that registered their 3LD the earliest will be entitled to own the 2LD.
For more information, check out Exabytes.