AbstractLetX(t),t≧ 0, be a real stationary Gaussian process, and, foru>0 andt>0, letLt(u) be the time spent byX(s), 0 ≦s≦t, above the levelu. Hereuis taken to be a functionu(t) oft, andLtis defined asLt(u(t)). It is shown that the distribution of (Lt–ELt)/(VarLt)1/2converges, fort→ ∞ andu(t) → ∞, to a standard normal distribution under various conditions relating the growth ofu(t) to the decay of the covariance and other functions ass