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We study the representation theory of Lie conformal analogues  r ( a ,  b ) of certain Galilean conformal algebras, whereare complex numbers. We first classify their finite irreducible conformal modules, and then solve the extension problem. In particular, we obtain several classes of new indecomposable conformal modules over  r ( a ,  b ).

Representations of Lie conformal algebras related to Galilean conformal algebras