Laplace integrals of the form
are considered for large values of z; f is holomorphic in a domain that contains the non-negative reals. The ratio is considered as a uniformity parameter in [0,. Integrals with the same asymptotic phenomenae are transformed into the above standard form by means of a canonical transformation. The analytic properties of this mapping are investigated, especially for the case that the mapping depends on . Error bounds for the remainders in the asymptotic expansions are given. Applications include a ratio of gamma functions, modified Bessel functions and parabolic cylinder functions. Analogue results are considered for loop integrals in the complex plane. This is the second paper in a series of three; the first paper has been published in Analysis 3, 221-249 (1983; Zbl 0541.41036).