Let Y be a nonsingular projective curve over an algebraically closed field k and f : X → Y a generically smooth semistable curve of genus g ≥ 2 with X nonsingular. Let ωX/Y denote the relative dualizing sheaf of f . Relation between deg ( f∗ωX/Y ) and discriminant divisors has been studied by many people. Here we consider the case of f hyperelliptic, i.e., the case where there exists a Y -automorphism ι inducing the hyperelliptic involution on the geometric generic fiber. Then for each node x of type 0 in a fiber, we can assign a non-negative integer, called the subtype, to x or the pair {x, ι(x)} (c.f. [CH] or §§ 1.2 for the definitions). Let δi(X/Y ) denote the number of the nodes of type i, ξ0(X/Y ) the number of nodes of subtype 0 and let ξj(X/Y ) denote the number of pairs of nodes {x, ι(x)} of subtype j > 0, in all the fibers. Cornalba and Harris proved in [CH] an equality