  The model under consideration is a two-dimensional two-component plasma,
i.e., a continuous system of two species of pointlike particles of opposite
charges $\pm 1$, interacting through the logarithmic Coulomb interaction. Using
the exact results for the form-factors of an equivalent Euclidean sine-Gordon
theory, we derive the large-distance behavior of the pair correlation functions
between charged particles. This asymptotic behavior is checked on a few lower
orders of its $\beta$-expansion ($\beta$ is the inverse temperature) around the
Debye-H\"uckel limit $\beta\to 0$, and at the free-fermion point $\beta = 2$ at
which the collapse of positive-negative pairs of charges occurs.
