Countersubject

Opening of Bach's Fugue no. 2 in C Minor from The Well-Tempered Clavier, Book I, BWV 847, showing the subject, answer, and countersubject (Benward & Saker 2009, 2:57).  Play 

When the first voice has completed the subject, and the second voice is playing the answer, the first voice usually continues by playing a new theme that is called the countersubject. The countersubject usually contrasts with the subject/answer phrase shape.

In a fugue, a countersubject is "the continuation of counterpoint in the voice that began with the subject", occurring against the answer (Benward & Saker 2009, 2:50). It is not usually regarded as an essential feature of fugue, however (Walker 2001).

The typical fugue opening resembles the following (Benward & Saker 2009, 2:50):

Soprano voice:               Answer        
Alto voice:       Subject    Countersubject

Since a countersubject may be used both above and below the answer, countersubjects are usually invertible, all perfect fifths inverting to perfect fourths which required resolution (Benward & Saker 2009, 2:51).

References

• Benward, Bruce, and Marilyn Nadine Saker. 2009. Music in Theory and Practice, eighth edition. 2 vols. + 2 CD sound discs. Boston: McGraw-Hill. ISBN 978-0-07-310188-0.
• Walker, Paul M. 2001. "Countersubject". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.