  We analyze several types of soliton solutions to a family of Tzitzeica
equations. To this end we use two methods for deriving the soliton solutions:
the dressing method and Hirota method. The dressing method allows us to derive
two types of soliton solutions. The first type corresponds to a set of 6
symmetrically situated discrete eigenvalues of the Lax operator $L$; to each
soliton of the second type one relates a set of 12 discrete eigenvalues of $L$.
We also outline how one can construct general $N$ soliton solution containing
$N_1$ solitons of first type and $N_2$ solitons of second type, $N=N_1+N_2$.
The possible singularities of the solitons and the effects of change of
variables that relate the different members of Tzitzeica family equations are
briefly discussed. All equations allow quasi-regular as well as singular
soliton solutions.
