The morning of our third and last day on the island I climbed a tower at the park entrance to watch the sunrise. The song of the church bells ringing in the campaniles blended with the throbbing sound of fishing boats churning out of the harbor. Halfway up a hillside east of the harbor someone had written ''TITO'' in block letters whiter than the limestone slope. President Tito's picture hung in almost every shop, but most people we met believed that Yugoslavia would continue to prosper without him.

''A people that has such youth need not fear for its future,'' read a quotation under Tito's picture in the Rab marketplace. By the time we left Rab in late September, the tourist season was over. We spent our last afternoon there swimming off the Frkanj Peninsula, and toward evening carried our bags down to the harbor past darkened hotels and restaurants with ''closed'' signs on their doors. The freshly washed streets were empty; their broad limestone paving blocks glistened in the lamplight. A small crowd had gathered to watch the fishing boats unload. Katja was waiting at her post under the streetlamp when the ferry to Hvar came in, and we said our goodbyes. As the boat slipped away, she was strolling homeward followed by a tired young couple swinging a rucksack between them.

The Liburnija is larger and more spacious than the Slavija, with two restaurants, a cafe and a swimming pool on her sundeck. The first-class cabins are large with windows and private showers, but our $30 off-season ticket did not buy one. For the overnight sail to Hvar we were packed into an airless compartment below the main deck where it required a gymnast's suppleness to climb into the bunks. When the boat docked in Split at dawn, we gratefully ran ashore for an hour to roam through the sprawling ruins of Diocletian's Palace and savor the mountains of watermelons, fresh cheeses and pomegranates in the open-air market near the docks.

The first thing that struck us as the ship approached Hvar was the turreted castle-fortress built on a hill. Its ramparts command a view of the town, the lavender-covered hills inland and the green islands that guard the harbor. Nudists and more modest bathers flock to the beaches on St. Jerolim and St. Klement, two islands served by a fleet of taxi-boats. After the quiet docks of Cres and Rab, the bustling hotel-lined harbor of Hvar was disconcerting. Although we knew that the season runs longer on the southern Adriatic islands, we were not prepared for a crowded international resort. The tourist bureau smugly refused to rent rooms in private homes for less than a week, but fortunately the women in the back streets were more accommodating. For $18, about $3 above the official rate, we found a room with a balcony overlooking the harbor.

Hvar was once a center of Croatian literary life. In its small 17th-century theater, now refurbished and open to the public, local playwrights presented their works. The arsenal below the theater, with its cavernous vaulted archway built for unloading Venetian galleons, is now a gallery of modern art. The Renaissance facade at the end of the harbor is all that remains of the count's palace, which was torn down in 1903 to make room for the Palace Hotel.

David was tiring of the steady diet of Wiener schnitzel, mixed grill and fish soup that we had found on the tourist menus since Opatija. A $4 bottle of Faros, the locally produced dry red table wine named after a fourth-century B.C. Greek settlement on the island, was the high point of an otherwise disappointing dinner at one of the brightly lit harborside restaurants.

At our next stop, Korcula, the massive stone walls jut into the Peljesac Channel like a ship's prow. We found a room in a private home near the bus station a few yards from the land gate, one of the three gates approached by broad stone staircases that provide the only access to the fortified town. Inside the walls, in a space no bigger than two city blocks, we found shells of stone houses burned out during the plague in 1529. Thick ivy crept through the windows of the abandoned house where Marco Polo, the island's most famous inhabitant, was born, but most of the original buildings had been beautifully restored.