In the presenc paper the notion "structure of a solution" as ciefired in [7] for an ordinary linear programming problem (1. p. problem) IS used to determine so-called uniqueness regions. Such a region is the set of all points of the parameter set yielding an ordinary 1. p. problern wit,h the same: uniquely refiner structure of the solution. Uniqueness regions are proved to be open sets in the parameter space and connections between them and stability regions as defined in [7] are stated. After introducing a certain regularity condition, which expresses that degeneracy always can bc overcome by slightly changing the parameters, it is shown, that the closure wit,h respect to the topology of the parameter space of any uniqueness region represents the corresponding stability region. I n the paper theoretical. fundamentals of parametric 1. p. problems with constant matrix of constraints are studied in order to classify parametric 1. p. problems of this kind having special parameter; dependence and to state common properties owing all problems of this type.