  `Hypergeometric states', which are a one-parameter generalization of binomial
states of the single-mode quantized radiation field, are introduced and their
nonclassical properties are investigated. Their limits to the binomial states
and to the coherent and number states are studied. The ladder operator
formulation of the hypergeometric states is found and the algebra involved
turns out to be a one-parameter deformation of $su(2)$ algebra. These states
exhibit highly nonclassical properties, like sub-Poissonian character,
antibunching and squeezing effects. The quasiprobability distributions in phase
space, namely the $Q$ and the Wigner functions are studied in detail. These
remarkable properties seem to suggest that the hypergeometric states deserve
further attention from theoretical and applicational sides of quantum optics.
