For every positive integer and every metric space we consider the class of all parametric families , where , , , of linear differential systems whose coefficients are piecewise continuous and, generally speaking, unbounded on the time semi-axis for every fixed value of the parameter such that if a sequence converges to in the space of parameters, then the sequence converges uniformly on the semi-axis to the matrix . For the families in , we obtain a complete description of individual Lyapunov exponents and their spectra as functions of the parameter.