One possibility is to have nonideal constant phase element CPE in parallel with a capacitance and a resistance. (Z_CPE)^{-1}=C/(jw)^n). Take a look to "Dielectric relaxation in solids" by A.K. Jonscher.

We used that description to fit depressed semicircle in J. Phys. Cond Matter 23 (2011) 496003

First of all non-ideal (Depressed semicircle) or deviation from Debye behavior and origin of different relaxations can be due to Grain orientation, Grain boundary, Sub-grain boundary, Electrode effect and also be due to Interface functional groups. Usually multiple relaxations can be associated with polycrystalline structure too.

You can observe these multiple relaxation from Cole-Cole plot, but some times this plot can't give you sufficient information. Then you can try Modulus plane plot or comparison between imaginary parts of M'' and Z''.

I hope my answer will serve your purpose.

Further you can look at these research papers

1) http://apl.aip.org/resource/1/applab/v101/i2/p023114_s1?isAuthorized=no

2) http://apl.aip.org/resource/1/applab/v101/i25/p253104_s1?isAuthorized=no

Cheers!

@ Kamran Rasool

Can you provide another link (or DOI, or full reference) for the articles, as I cannot use the links you provided?

Thank you in advance