Prediction of gaseous transport properties requires calculation of Chapman–Enskog collision integrals which depend on all possible binary collision trajectories. The interparticle potential is required as input, and for a variety of applications involving monatomic gases the Hulburt–Hirschfelder potential is useful since it is determined entirely from spectroscopic information and can accomodate the long-range maxima and minima found in many systems. Hulburt–Hirschfelder potentials are classified into five distinct types according to their qualitative binary collision dynamics, which in general can be quite complex and can exhibit ’’double orbiting’’, i.e., a pair of orbiting impact parameters for a single energy of collision. The collision integral program of O’Hara and Smith has been revised extensively to accomodate all physical cases of the Hulburt—Hirschfelder potential, and the required numerical methods are described and justified. The revised program substantially extends the range of potentials for which collision integrals can be calculated.