In C the result of the prefix and postfix increment/decrement operators is not an lvalue.
In C++ the result of the postfix increment/decrement operator is also not an lvalue but the result of the prefix increment/decrement operator is an lvalue.
Now doing something like (++a)--
in C++ is undefined behavior because you are modifying an object value twice between two sequence points.
EDIT: following up on @bames53 comment. It is undefined behavior in C++98/C++03 but the changes in C++11 on the idea of sequence points now makes this expression defined.