1/f noise is shown to be generated by systems with random transitions between discrete states with distributed transit probabilities. A hidden discrete key process is driving the observable process which appears to be continuous. The key process is a non-homogeneous Poisson process. The observable process consists of sums of random increments generated by the key process in all time intervals considered. Provided, the key process is characterized by a linearly increasing intensity function and causes random increments which are independent and identically distributed, the observed process shows the typical 1/f fluctuation. The intensity function of the key process increases linearly if the distribution of transit probabilities approaches zero in a way that its reciprocals (return periods to the individual transits) are (at least in the upper tail) exponentially distributed. The paper concludes with the suggestion, that the crucial 'upper tail exponentiality' is a general asymptotic property.
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