Mechanisms influencing learning in neural networks are usually investigated on either a local or a global scale. The former relates to synaptic processes, the latter to unspecific modulatory systems. Here we study the interaction of a local learning rule that evaluates coincidences of pre- and postsynaptic action potentials and a global modulatory mechanism, such as the action of the basal forebrain onto cortical neurons. The simulations demonstrate that the interaction of these mechanisms leads to a learning rule supporting fast learning rates, stability, and flexibility. Furthermore, the simulations generate two experimentally testable predictions on the dependence of backpropagating action potential on basal forebrain activity and the relative timing of the activity of inhibitory and excitatory neurons in the neocortex.