In music, a countersubject is a melodic or thematic idea which is played against a primary subject of a fugue

Fugue

In music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....

, ricercar

Ricercar

A ricercar is a type of late Renaissance and mostly early Baroque instrumental composition. The term means to search out, and many ricercars serve a preludial function to "search out" the key or mode of a following piece...

, invention, sinfonia

Sinfonia

Sinfonia is the Italian word for symphony. In English it most commonly refers to a 17th- or 18th-century orchestral piece used as an introduction, interlude, or postlude to an opera, oratorio, cantata, or suite...

, or other contrapuntal

Counterpoint

In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent . It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period,...

 piece of music. Generally a countersubject contrasts in character to a principal subject, so if the primary subject is a stately one in long note values, the countersubject is likely to be rhythmically more active, and vice-versa.

In a work which is not formally contrapuntal, i.e. not a fugue or an invention, a secondary theme playing against a primary theme is usually termed a countermelody

Counter-melody

In music, counter-melody is a sequence of notes, perceived as a melody, written to be played simultaneously with a more prominent lead melody. Typically a counter-melody performs a subordinate role, and is heard in a texture consisting of a melody plus accompaniment...

.

It is usually opposite of the subject.