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I want to run a script from a server from my local. I am managing tomcat application and I wanted to run startup.bat and shutdown.bat remotely via batch script.

For now I was trying to use Psexec tools but I was having problem as the batch file I'm trying to call, executes many batch files inside the server.

Note: tomcat is not installed as service on the server.

Well we are not omniscient so unless you can show us how you are trying to use psexec and the code in the other batch files as well as any error messages you are getting it will be kind of hard for anyone to help you troubleshoot.
Another option is to use WinRS.