Generics with Generic Parameters and Abstract class

In my experience it is easiest to create non-generic interface to generic classes. It also solves the problem when you need to cast to the base class without knowing the generic type.

interface IFirstClass {...}

abstract class FirstClass<T> : IFirstClass {...}

abstract class SecondClass<T> where T : IFirstClass {...}

If you are actually using the generic type arguments to FirstClass (as, from your edit, it sounds like you are), then no, what you're looking for is unfortunately not possible. The compiler does not differentiate between type arguments that are related and those that are not.

Create an interface that FirstClass implements. Then you can constrain SecondClass to the interface.