North and South Korea, after a series of false starts, are in the midst of a complex, five-channeled dialogue covering issues ranging from trade to reunification of families separated by the Korean War.

To date, the talks have accomplished nothing of substance, and many people here expect them to break down, as have all previous discussions between the two intensely hostile governments.

Still, coupled with changes in the geopolitical relations surrounding the Korean Peninsula, the talks have led to hopes that some type of meaningful reduction of tension could result.

The latest development came this morning when South Korean Sports Minister Lee Yong Ho rejected a proposal from the North that the 1988 Summer Olympics, scheduled to be held in Seoul, be hosted jointly in the North and South. Lee did agree to discuss a single North-South Olympic team, however.

The five sets of negotiations are proceeding slowly, with meetings most often being held at the truce village of Panmunjom in the Demilitarized Zone that divides the Korean Peninsula.

The issues include:

*Economic cooperation. The two sides have agreed to set up a commission to oversee the reopening of trade and investment between the zones, which were suspended before the Korean War began in 1950. Discussions will continue on Sept. 18.

*Family reunification. The Red Cross societies of North and South have agreed in principle to allow visits between separated family members in September. However, the sides are deadlocked on where the reunions would take place. On Aug. 27, a South Korean delegation is expected to go to Pyongyang, the North's capital, for more discussions on humanitarian issues.

*Parliamentary cooperation. Last month, legislators from the two sides, conducting a preliminary meeting in Panmunjom, failed to agree on a subject for full talks but agreed to meet again on Sept. 28.

*Sports cooperation. In October, the two sides are expected to meet in Switzerland to discuss joint activities at the 1988 Olympics.

*Military disengagement at Panmunjom. Last month, the North proposed that the two sides remove heavy weapons and fortifications from the area around the meeting site and reduce the number of guards from 65 to 30 on each side. The United Nations Command, which coordinates U.S. and South Korean troops, agreed to study the matter.

The scope and frequency of the discussions are unprecedented. The idea is that by starting with small issues, the two sides can build trust that will allow them to move on to the substantive military and political questions that divide Korea.

Seoul continues to view the talks with suspicion. One government official here said the North's true intention is to create just enough trust to open a direct channel of discussions with the United States and bypass the South.

The North's long-established stance is that the removal of U.S. troops from the South must be the first step toward real reconciliation. The United States and the South have refused, saying the troops are needed to deter an invasion from across the Demilitarized Zone.

Hopes for real progress today stand somewhat higher because of pressure on both sides from their patron countries, the United States and Japan for the South, and China and the Soviet Union for the North.

The dialogue is full of political pitfalls. Although the Korean War ended 32 years ago, the two sides have remained almost totally sealed off from one another. The meetings generally open with ritual smiles and talk of Korean brotherhood, but once discussions begin, both sides treat the most minute detail with suspicion and an eye to propaganda.