The paper is devoted to study the $n$th Hawaiian group $\mathcal{H}_n$, $n \ge 1$, of the wedge sum of two spaces $(X,x_*) = (X_1, x_1) \vee (X_2, x_2)$. We are going to give some versions of the van Kampen theorem for Hawaiian groups of the wedge sum of spaces. First, among some results on Hawaiian groups of semilocally strongly contractible spaces, we present a structure for the $n$th Hawaiian group of the wedge sum of CW-complexes. Second, we give more informative structures for the $n$th Hawaiian group of the wedge sum $X$, when $X$ is semilocally $n$-simply connected at $x_*$. Finally, as a consequence, we study Hawaiian groups of Griffiths spaces for all dimensions $n\geq 1$ to give some information about their structure at any points.

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