The article essays analysis of exclave phenomenon as one of the varieties of territoriality — spatial expression of political organization. On discussing the existing typologies of enclaves/exclaves and on proposing his own classification of enclave territories, the author investigates in detail the complex of problems being engendered by “intermittent” exclave territoriality, with special consideration of problems related to access, political governance, economic development, and identity. Significant attention is given in the article to investigating the evolution of exclaves under globalization. Stating the tendency to the turning of such formations into regions-subjects, the author sees in its development the pledge of efficient progress of the largest Russian exclave — Kaliningradskaya oblast.