Femtosecond X-ray pulses are a powerful tool to investigate atomic motions triggered by femtosecond pump pulses. This thesis is dedicated to the production of such pulses and their use in optical pump – X-ray probe measurement. This thesis describes the laser-plasma-based sources available at the University of Duisburg-Essen. Part of it consists of the description of the design, built-up and characterization of a new “modular” X-ray source dedicated to optimize the X-ray flux onto the sample under investigation. The acoustic wave generation in femtosecond optically excited semiconductor (gallium arsenide) and metal (gold) was performed using the sources of the University of Duisburg-Essen. The physical answer of the material was modeled by a simple strain model for the semiconductor, pressure model for the metal, in order to gain information on the interplay of the electronic and thermal pressures rising after excitation. Whereas no reliable information could be obtain in gallium arsenide (principally due to the use of a bulk), the model for gold achieved very good agreement, providing useful information. The relaxation time of the electron to lattice energy was found to be (5.0±0.3) ps, and the ratio of the Grüneisen parameters was found to be e / i = (0.5±0.1). This thesis also describes the Sub-Picosecond Pulse Source (SPPS) which existed at the (formally) Stanford Linear Accelerator Center, an accelerator-based X-ray source, and two measurements performed with it. The first one is the detailed investigation of the phonon softening of the A1g mode launch in bismuth upon fluence excitation. Detailed information concerning the new equilibrium position and phonon frequency were obtained over extended laser pump fluences. The second measurement concerned the study of the liquid phase dynamics in a newly formed liquid phase following ultrafast melting in indium antimonide. The formation of the liquid phase and its development for excitations close to the ablation threshold were revealed. Such results were possible to obtain, due to the unprecedented combination of a short X-ray pulse duration and brightness at the SPPS.