I have SDL Tridion 2011 SP1 installed. But the Delivery environment is of 2011 GA version installed on Windows 2008 R2 SP1 server. So I have hybrid version running in my system.
Now I want to upgrade to SDL Tridion 2013 completely.
I am planning to first upgrade Delivery services to 2011 SP1 version. Later I am planning to do update from 2011 SP1 to 2013.
I am not sure of the compatibility issues that I could face.
Please suggest me the precautions for this.
I agree with Jaime and best to upgrade both CM and CD to 2013. It will also help any customer support requests that you make. The Java pre-reqs are different between 2011 and 2013.
The 2011 -> 2013 upgrade is a minor one with no major architecture changes (except removing COM+ under the CMS), compared to the 2009 -> 2011 upgrade, which is a major one where many pieces of the architecture changed (Content Delivery, Event System, Core Services, etc).
Best to upgrade the Dev / Test environments 100% (CM + CD) and document the versions required (JRE) and also all steps needed for the upgrade. I assume you are using VBScript or something COM+ related, so plan on installing the optional Legacy pack for COM+ and VBScript. In that case, all the code you have will be compatible and only need a good test plan to cover publishing, event system, and content delivery broker queries.
It should work if you have a regular Tridion install. However I do see issues in you have installed products like Experience Manager, UGC or any product that is dependent on the Content Delivery Web Service to Push Data or Fast Track Publish. These products need direct connectivity between the CM side and the CD side via a POST method. In case you have different versions for CM and CD you will probably have issues regarding incompatible Web Services calls (POST).
You shouldn't have Hybrid setups. It is a bad practice to upgrade your environment only partially. Even if as Nuno states you might not find any issue (Tridion typically supports mixed versions of Delivery as a way to help upgrading, it's really not meant to work long term) it is also possible that you might find some.
What I would recommend is to upgrade both to 2013 ASAP or if you are not ready for such an upgrade, at least you make sure you upgrade your CD GA to SP1, too. I had to deal with a few requests in the past regarding what jar version is the right one... and if you don't do the upgrade from the beginning you can end up with a messy environment.
Again, try avoiding these hybrid scenarios, because I don't believe they are supported.
The staged upgrade Jaime mentions is described in a little more here: http://www.building-blocks.com/thinking/upgrading-to-sdl-tridion-2013-the-staged-upgrade/
It is a stepping stone, and should not be used for an extended period of time. As quickly as possible you should fully transition to matching versions of both Content Manager and Content Delivery.
Otherwise I don't see any issues with your upgrade.
Please double check prerequisites as they are different from Tridion 2011 GA/SP1 to Tridion 2013.
