Authors’ abstract: We investigate the spectrum for \(\{4\}\)-GDDs of type \(g^u m^1\). We determine, for each even \(g\), all values of \(m\) for which a \(\{4\}\)-GDD of type \(g^u m^1\) exists, for every ‘fourth’ value of \(u\). We similarly determine, for each odd \(g\neq 11\) or \(17\), all values of \(m\) for which a \(\{4\}\)-GDD of type \(g^u m^1\) exists, for every ‘third’ value of \(u\). Finally, we establish, up to a finite number of values of \(u\), the spectrum for \(\{4\}\)-GDDs of type \(g^u m^1\) where \(gu\) is even, \(g\not\in\{11, 17\}\).