This paper presents a probabilistic approach to the characterization of dynamic properties of harmonics in power systems. In this framework it is assumed that, in addition to a deterministic component, harmonics contain a stochastic component that is modeled by a Markov chain. This mathematically tractable approach enables a power system analyst to study dynamics of harmonics, while accommodating the possibility that the underlying stochastic process may have a finite memory. The suggested framework thus removes the uncorrelated-ness ("whiteness") assumption for the temporal evolution of harmonics, which is often not supported by actual measurements. Mathematical formulae to compute the first and second moments of the resulting random waveforms are presented for the practically relevant case of finite-dimensional discrete-time Markov chains. The approach is illustrated on computer simulations and on actual data taken from a residential load.