Technically - cave resuce is classified as a confioned space rescue. IN SA - SAPOL STAR and SES (Noarlunga and Whyalla) have trained, accredited and equiped teams for this. I believe there are also limited trained persons within MFS.
As we all know thought, there are many different style of caves - open, sink holes, verticle, horizontel and then those filled with H2O.
Guss in first instance a verticle team from SES, SAPOL or CFS could begin, however if in a hazardous environment or confined then a specialist team would be required.