Identification of dynamical systems is, in essence, a problem of observability of system parameters from a related Bet of observations. In this article, a necessary and sufficient condition is obtained for the observability of parameters from a given record of inputs and states of a linear system with a class of parameter variations. Also obtained is n necessary and sufficient condition of observability of a Sub-class of such systems with polynomial system and constant output coefficient matrices when only the outputs instead of the states are accessible for measurement.