A slight slowing down or speeding up of the tempo characteristically employed in the performance of much romantic music is?

Rubato: Literally means "robbed" in Italian, and has a flexible tempo. The timing or tempo is relaxed and is close but not strictly on the beat.

Rubato can be heard in pieces such as Debussy's "Clair de Lune" or Chopan's "Polonaise in A-flat major, Op. 53".