The influence of space charge on emittance growth is studied in simulations of a coasting beam exposed to a strong octupolar perturbation in an otherwise linear lattice, and under stationary parameters. We explore the importance of self‐consistency by comparing results with a non‐self‐consistent model, where the space charge electric field is kept “frozen‐in” to its initial values. For Gaussian distribution functions we find that the “frozen‐in” model results in a good approximation of the self‐consistent model, hence coherent response is practically absent and the emittance growth is self‐limiting due to space charge de‐tuning. For KV or waterbag distributions, instead, strong coherent response is found, which we explain in terms of absence of Landau damping. © 2003 American Institute of Physics