Particle aspects of two-dimensional conformal field theories are investigated, using methods from algebraic quantum field theory. The results include asymptotic completeness in terms of (counterparts of) Wigner particles in any vacuum representation and the existence of (counterparts of) infraparticles in any charged irreducible product representation of a given chiral conformal field theory. Moreover, an interesting interplay between infraparticle's direction of motion and the superselection structure is demonstrated in a large class of examples. This phenomenon resembles electron's momentum superselection expected in quantum electrodynamics.