In certain conditions, filamentous fungi are observed to grow exponentially during batch submerged growth. It is shown for three cases, with simple mechanistic models, that an exponential growth assumption is reasonable. The basis of these models is the identification of a growth unit, and a mechanism for its doubling with a constant generation time. The importance of the variation of morphological properties within populations is demonstrated by the comparison of computer simulations of simplified models using average values and either experimental data or computer simulations of detailed stochastic models.