  We have investigated the properties of a model of 1D anyons interacting
through a $\delta$-function repulsive potential. The structure of the
quasi-periodic boundary conditions for the anyonic field operators and the
many-anyon wavefunctions is clarified. The spectrum of the low-lying
excitations including the particle-hole excitations is calculated for periodic
and twisted boundary conditions. Using the ideas of the conformal field theory
we obtain the large-distance asymptotics of the density and field correlation
function at the critical temperature T=0 and at small finite temperatures. Our
expression for the field correlation function extends the results in the
literature obtained for harmonic quantum anyonic fluids.
