Monk Anthony withdrew himself from the monastery and later settled on a new hill, where he dug out a new underground cell, now called the Near Caves.

The caves also have a total of 79 surviving burials, among them being Nestor the Chronicler, the icon artists Alipy and Grigory, the doctor Agapit, the prince-ascetic Nikolai Sviatosha, the holy martyr Kuksha, as well as the remains of the epic hero Ilya Muromets.

[2] The Near Cave's main temple is the Church of the Elevation of the Cross (Khrestovozdvizhenska), which was constructed in the Ukrainian Baroque style from 1700-1704.

The old refectory of the church is connected to the brother's cells, a Neoclassical style building with a four-column portico dating from the 1830s.

At the foot of the hill stands the Near Cave's belltower, which was designed and constructed by architect Stepan Kovnir in 1760.