Pump-probe spectroscopy combined with laser and synchrotron radiation is performed to study the ionization and dissociation dynamics of N-2 and N2O in the extreme ultraviolet energy region. The N-2(+)(X(2)Sigma(g)(+) ,v, N) ion produced from N-2 or N2O by synchrotron radiation excitation is detected by laser-induced fluorescence (LIF) spectroscopy. To increase the number density of ions produced by synchrotron radiation photoexcitation, a cylindrical ion trap cell is employed. The effect of thermalization on the internal state distributions of N-2(+) ion can be ignored in the ion trap. The rotational structure of the electronic excitation B(-2)Sigma(u)(+), v' = 0, N' <-- X(2)Sigma(g)(+), v" = 0, N" of N-2(+) produced from N-2 is clearly resolved by using a narrow-bandwidth Ti:sapphire laser. The yield curves for N-2(+)(X(2)Sigma(g)(+), v = 0, 1) are also measured as a function of the photon energy of the synchrotron radiation. The rotational temperature of N-2(+)(X(2)Sigma(g)(+), v = 0) produced from N2O+((BII)-I-2) is determined from a LIF spectrum to be in the range 200-230 g. The analysis based on the impulsive model indicates that the equilibrium bond angle of the vibrational ground state of N2O+((BII)-I-2) is > 160 degrees.