How does a double fugue use two subjects?

A double fugue is a musical composition that utilizes two subjects, which are treated both separately and simultaneously.1

There are two primary ways composers approach this structure:

• Simultaneous Exposition: The two subjects are introduced at the same time. This method functions similarly to a simple fugue that incorporates a countersubject.2
• Separate Expositions: More commonly, the composer provides each subject with its own complete, independent exposition. The two subjects are then eventually brought together later in the piece.2

In some instances, such as in Mozart’s Fugue in G Minor, K 401, the two subjects may be melodic inversions of one another. The use of counterpoint remains essential to maintaining clarity when these two distinct themes are combined.2