We consider the multiset construction of decomposable structures with component generating function C(z) of alg-log type, i.e., align* C(z) = (1-z)-α(log1 / 1-z)β. align* We provide asymptotic results for the number of labeled objects of size n in the case when α is positive and β is positive and in the case α= 0 and β≥2 . The case 0<-α<1 and any β and the case α> 0 and β= 0 have been treated in previous papers. Our results extend previous work of Wright.