  We present exact solutions describing dynamics of two algebraic solitons in
the massive Thirring model. Each algebraic soliton corresponds to a simple
embedded eigenvalue in the Kaup--Newell spectral problem and attains the
maximal mass among the family of solitary waves traveling with the same speed.
By coalescence of speeds of the two algebraic solitons, we find a new solution
for an algebraic double-soliton which corresponds to a double embedded
eigenvalue. We show that the double-soliton attains the double mass of a single
soliton and describes a slow interaction of two identical algebraic solitons.
