The paper reports on measurements and analysis of the measurements during hardening and drying of specimens using selected acoustic nondestructive testing techniques. An integrated approach was created for better understanding of the relations between the lifetime cycle and the development of the mechanical properties of concrete. Acoustic emission, impact echo, and ultrasonic techniques were applied simultaneously to the same mixtures. These techniques and results are presented on alkali-activated slag mortars. The acoustic emission method detects transient elastic waves within the material, caused by the release of cumulated stress energy, which can be mechanical, thermal, or chemical. Hence, the cause is a phenomenon which releases elastic energy into the material, which then spreads in the form of an elastic wave. The impact echo method is based on physical laws of elastic stress wave propagation in solids generated by mechanical impulse. Ultrasonic testing is commonly used to find flaws in materials or to assess wave velocity spreading.