This paper is in continuation of computation to arbitrary precision of hyperterminants that occur in hyperasymptotic expansions for solutions to second-order linear differential equations and integrals with two saddles [the author, part I, J. Comput. Appl. Math. 76, No. 1-2, 255-264 (1996; Zbl 0866.65011
)]. The author concerns the computation of the hyperterminants that occur in hyperasymptotic expansions of higher-order linear differential equations, nonlinear differential equations and integrals with more than two saddles. The author gives new integral representations for the hyperterminants. With these integral representations, the author is able to obtain convergent and computable series expansions for hyperterminants. Another feature of the results is the occurence of hypergeometric functions.