The stability of a large variety of insect populations was studied using 14 years of light-trap data collected in a relatively undisturbed tropical forest in Panama. Special emphasis was placed on trends in abundance over time. A large between-species variation was found in stability, ranging from nearly constant to violently fluctuating. Over a 14-year period 22% of the species with more than 26 individuals caught showed an average trend of more than 10% of their mean abundance per year, and 4% a trend of more than 20% per year. Even among the 78 species represented by more than 1000 individuals, 7 species, 9%, showed a trend of more than 10% of mean abundance per year. These results appear to be incompatible with the generally held tenet that natural populations in undisturbed environments fluctuate within rather narrow abundance limits, and may indicate that at least a certain proportion of natural populations are not kept within such limits by regulatory processes. Actual fluctuating patterns vary a great deal between species, suggesting the absence of some dominant environmental process affecting several species at the same time. The total number of species and individuals, and the associated value of the Ξ±-diversity index remained at the same level over the 14 years.