In this paper we analyzed how connectivity (defined as number of connections between network elements) can affect the memory capacity of a network-based model of the Immune System (IS) and of a model of the Nervous System (NS) synaptic plasticity (BCM model). The key point is the concept of competition between the characteristic variables that represent the response of such systems to environmental stimuli: the clonal concentrations for the IS, and the neuron responses for the BCM model. The memory states of both systems are characterized by a high selectivity to specific input patterns, reflecting a similar behaviour of their development rules. This selectivity property of memory states can be controlled by changing the degree of the internal connectivity in each system. We can explain the changes occurring in IS memory states during lifespan as due to a reshaping of its internal connectivity. This assumption is in agreement with experimental observations, reporting an increase of IS memory cells during lifespan. The change of connectivity in the BCM model leads to the introduction of quasilocal variables governing the plasticity of groups of synaptic junctions. This could be interpreted as the result of a refinement of neuron internal mechanisms during development, or it could be seen as a different learning rule deriving from the original BCM theory. We argue that connectivity seems to play an important role in a large class of biological systems controlled by competition mechanisms. Moreover, changes in connectivity may lead to changes in memory properties during development and aging.