The article is devoted to algorithms for measuring the oscillatory-dissipative characteristics of integrating solid-state wave gyroscoperesonators. The list of such algorithms is limited only to algorithms that use the results of transient processobservation of free oscillations after excitation of a pronounced standing wave in a resonator. The list of measured oscillation-dissipative characteristics includes the values of different frequencies and different Q ratios of gyroscope resonators, as well as angular positions of the stiffness and Q-axes. The article contains sequentially performed a mathematical description of the mode of free run-out of standing waves in the gyroscope resonator; mathematical description of the signalinternal structure generated by the gyroscopemeasuring device; preliminary analysis of the initial data and quantitativeparameterassessment for the physical representation of the resonatorfree oscillation features. On this basis, variousdetailing algorithm options to assess the resonatorstiffness properties for observing transient processes in the free run-out mode of the wave pattern are discussed, as well as possible approaches to the algorithmconstruction to assessresonator viscosity properties. The givenalgorithm formulations are focused on the use of standard two-channel measuring gyroscopedevice, capable to calculate the angle and amplitudes of standing working and quadrature waves. It has been confirmed that the observation of transients in time in the free run-out mode of the wave pattern makes it possible to obtain fairly simple computational algorithms to assess the resonatorstiffness properties. At the same time, in order to measure the disparity and angular position of the viscosity axes of the resonator when observing transient processes, a more complex computational identification problem is required. For the practical application of the above-mentioned algorithms to measure the different frequency and angular position of the stiffening axes, the observation time interval should be selected based on the calculation that the multiphase of the resonant oscillations exceeds half of the wavelength .