In the course of study of dendroids, Czuba [3] introduced a notion of

-continua which is a generalization of R-arc [1]. He showed a new class of non-contractible dendroids, namely of dendroids which contain an

-continuum. Subsecequently Charatonik [2] attempted to extend the notion into hyperspace C(X) of metric continuum X. In so doing, there were some oversights in extending some of the results relating

-continua of dendroids for metric continua. In fact, Proposition 1 in [2] is false (see example C below) and his proof of Theorem 6 in [2] is not correct (Take Example 4 in [4] with K = [e,e'] as an

-continuum of X and work it out. Then one seens that K not .mem. K as he claimed otherwise.). The aims of this paper are to introduce a notion of w-regular convergence which is weaker than 0-regular convergence and to prove that the w-regular convergence of a sequence {Xn}

to

of subcontinua of a metric continuum X is a necessary and sufficient for the sequence {C(

)}

to converge to C(

), and also to prove that if a metric continuum X contains an

-continuum with w-regular convergence, then the hyperspace C(X) of X contains

-continuum.inuum.uum.