Using image analysis the growth kinetics of the single hyphae of the filamentous fungus Aspergillus oryzae has been determined on-line in a flow-through cell at different glucose concentrations in the range from 26 mg L-1 to 20 g L-1. The tip extension rate of the individual hyphae can be described with saturation type kinetics with respect to the length of the hyphae. The maximum tip extension rate is constant for all hyphae measured at the same glucose concentration, whereas the saturation constant for the hyphae varies significantly between the hyphae even within the same hyphal element. When apical branching occurs, it is observed that the tip extension rate decreases temporarily. The number of branches formed on a hypha is proportional to the length of the hypha that exceeds a certain minimum length required to support the growth of a new branch. The observed kinetics has been used to simulate the outgrowth of a hyphal element from a single spore using a Monte Carlo simulation technique. The simulations shows that the observed kinetics for the individual hyphae result in an experimentally verified growth pattern with exponential growth in both total hyphal length and number of tips.