Atomic clocks exhibit the highest performance levels as far as time/frequency accuracy and stability are concerned, moreover show reliability and lifetime which makes them undisputable references in modern applications such as telecommunication networks and navigation systems. However their stability is affected by environmental factors, by aging and by component damages. In this second paper attention is paid to the estimate of frequency instability introduced by deterministic processes as drifts or periodic modulations and by variations of device characteristics due to aging or failures. It is important therefore to use techniques to analyze and to define the clock stability as a function of time, that is under non-stationary conditions. According to the problem under discussion the analysis is carried out by exploiting the properties of the modified Hadamard variance weighed with binomial coefficients or the use of the Dynamic Allan Variance (DAVAR). Moreover the Total variance method (Totvar) to face the problem of a limited number of data available for statistical evaluation of slowly varying noise is described. A few examples are given with simulated or real experimental data.