Summary: A bull is a graph which is obtained by attaching two edges to two vertices of a triangle. A bull-design of order \(n\) is an ordered pair (\(X,\mathcal A\)), where \(X\) is the vertex set of \(K_{n}\) and \(\mathcal A\) is an edge-disjoint decomposition of \(K_{n}\) into copies of bulls.
In this paper, it is shown that a bull-design of order \(n\) can be embedded in a bull-design of order \(m\) if and only if \(m\geq 3n/2+1\) or \(m=n\). This produces a generalization of the Doyen-Wilson theorem for bull-designs.