Please provide some details about the Linux versions, and whether you use 32 or 64 bit distributions. In addition to this please post (attach) the vmware.log files for the virtual ESXi host as well as for one of the nested Linux VMs.
Hard to say what's causing the issue without the log files.
You may also want to take a look at Running Nested VMs to see what needs to be configured in order to be able to install and run nested 64-bit guests.
You might want to try installing CentOS with the RedHat 5.x O/S choice for the VM instead of RedHat 6.x and see if that gets you installed.
Assuming this is ESX 5.x as the physical ESX host and your CPU has RVI or EPT capability, the O/S choice I'm referring to would be the choice for the O/S for the VM to use (not your choice of Linux for the VM that runs in the O/S). Under Edit Settings for the VM, go to the Options Tab and choose General Settings and in the bottom right side -- choose RedHat 5.x instead of RedHat 6.x.
You may have to build a fresh VM (rather than using your existing VMs and changing the O/S type to RedHat 5.x).
Message was edited by: Datto