A turbomachine dual spool transmission system can include a direct drive assembly configured to selectively allow bypassing of a dual spool differential combination output to allow selective direct engagement of a low pressure spool to directly drive a rotational member or to be directly driven by the rotational member. The system can include the dual spool differential. The dual spool differential can include a gear assembly configured to combine a low pressure spool input and a high pressure spool input into a combination output to provide an output speed range smaller than a low pressure speed range alone.