  Exceptional extensions of a class of Laurent biorthogonal polynomials (the
so-called Hendriksen-van Rossum polynomials) have been presented by the authors
recently. This is achieved through Darboux transformations of generalized
eigenvalue problems. In this paper, we discuss the recurrence relations
satisfied by these exceptional Laurent biorthogonal polynomials and provide a
type of recurrence relations with $3l_0+4$ terms explicitly, where the
parameter $l_0$ corresponds to the degree of the polynomial part in the seed
function used in the Darboux transformation. In the proof of these recurrence
relations, the backward operator which maps an exceptional polynomial into a
classical one plays a significant role.
