Abstract: Lagally (1929) has given the exact solution for the two dimensional incompressible potential flow indued by two fixed circles in a uniform stream. In this paper, three exact solutions are obtained for two dimensional incompressible potential flow induced by two circles moving or expanding in a still fluid in three cases: (i) expansion (or contraction) of themselves, (ii) approach to (or departure from) each other, (iii) their movements perpendicular to the connected-centre-line in opposite directions.