An extensive study of the superconducting properties of the ternary graphite intercalation compounds has been carried out, with special emphasis on the potassium-mercury (KHg) and cesium-bismuth (CsBi) systems. The specimens were synthesized using a variety of conditions, and an effort was made to correlate the preparation conditions with the superconducting properties. Superconducting transition temperatures Tc between 0.7 and 1.5 K are found for C4KHg, while no superconductivity was observed in the compound C4CsBix, contrary to previous reports. For C4KHg lower transition temperatures and broader superconducting transitions are associated with the presence of the minority beta phase. Neutron and x-ray diffraction analysis show no significant difference between the majority alpha-phase regions in the lower- and higher-Tc specimens. The increase of Tc in the KHg-GIC's with increasing stage (and therefore decreasing intercalant concentration) is in contradiction to expectations from theories of the superconducting proximity effect. The trend of Tc in the KHg-GIC's is interpreted as evidence for the participation of both graphitic and intercalant electrons in the superconductivity. The upper critical field phase boundary Hc2(theta, T) was measured on both types of C4KHg specimens. The probable observation of type I superconductivity for some field orientations is reported for the Tc = 1.5 K samples. The critical field data are analyzed in terms of the anisotropic Ginzburg-Landau model, and evidence for extended linearity of Hc2(T) and temperature-dependent anisotropy is presented. Comparisons to more detailed models of anisotropic superconductivity are made where appropriate. Hydrogenation experiments on C4KHg show a dramatic increase in Tc, quite similar to a Tc enhancement seen under applied pressure. The effect of hydrogenation is tentatively explained to be the suppression of a charge-density wave state. This assignment is made by analogy to the transition metal dichalcogenides, which have many features in common with the superconducting GIC's. Possible reasons for the lack of superconductivity in the CsBi compounds are discussed, with an emphasis on implications for the other superconducting GIC's.