We continue the study of semi-weakly continuum-chainable continua, weakly continuum-chainable continua and continuum-chainable composants. We introduce two new classes of continua, namely, semi-almost continuum-chainable and almost continuum-chainable continua and a new type of composants named union composants, which are related to continuum-chainable composants, but they are different and we give an example showing this.