We present recent results of x-ray laser amplification of spontaneous emission in Ne-like and Ni-like transient collisional excitation schemes. The plasma formation, ionization and collisional excitation can be optimized using two laser pulses of 1 ns and 1 ps duration at table-top energies of 5 J in each beam. High gain of 35 cm−1has been measured on the 147 Å4d→4pJ=0→1transition of Ni-like Pd and is a direct consequence of the nonstationary population inversion produced by the high intensity picosecond pulse. We report the dependence of the x-ray laser line intensity on the laser plasma conditions and compare the experimental measurements with hydrodynamic and atomic kinetics simulations for Ne-like and Ni-like lasing. ©1998 American Institute of Physics.