  We investigate the particle-number fluctuations due to the collective
excitations created in a two-dimensional (2D) and a quasi-2D Bose-Einstein
condensates (BECs) at low temperature. We find that the fluctuations display an
anomalous behavior, i. e. for the 2D BEC they are proportional to $N^2$, where
$N$ is the total number of particles. For the quasi-2D BEC, the particle-number
fluctuations are proportional not only to $N^2$ but also to the square root of
the trapping frequency in the strongly-confined direction.
