Requirements for future high-density recording media are discussed. Simple formulae are given to estimate the effect of media parameters such as coercivity, magnetization, film thickness as well as grain size on achievable areal density. It is found that reducing the grain size is the most important single factor for achieving higher storage densities. A reduction of grain size leads to a strong time dependence of coercivity and will eventually lead to superparamagnetic behavior. We present experimental data on the time dependence of coercivity in the range from 5 ns up to a few 100 mu s. A simple formula, which takes the random grain orientation in the media into account, is derived and shown to describe the experimental results more satisfactory than previous theories. Furthermore, we investigate very thin films and show experimental evidence for transition broadening. A simple theoretical estimation shows that, for current media materials, (cubical) grains in the range of 10-14 nm are predicted to be thermally stable. (C) 1999 Published by Elsevier Science B.V. All rights reserved.