In this paper, two new families of constructive Self-Organizing Maps (SOMs), SAM-SOM* and MAM-SOM*, are proposed. These families are specially useful for information retrieval from large databases, high-dimensional spaces and complex distance functions which usually consume a long time. They are generated by incorporating Spatial Access Method (SAM) and Metric Access Method (MAM) into SOM with the maximum insertion rate, i.e. the case when a new unit is created for each pattern presented to the network. In this specific case, the network presents interesting advantages and acquires new properties which are quite different of traditional SOM. In a constructive SOM, if new units are rarely inserted into network, the training algorithm would probably need a long time to converge. On the other hand, if new units are inserted frequently, the training algorithm would not have enough time to adapt these units to the data distribution. Besides, training time is increased because the search for the winning neuron is traditionally performed sequentially. The use of SAM and MAM combined with SOM open the possibility of training constructive SOM with as much units as existing patterns with less time and interesting advantages compared with both models: Kohonen network SOM and SAM-SOM model (SOM using SAM). Advantages and drawbacks of these new families are also discussed. These new families are useful to improve both SOM and SAM techniques.