We present a detailed study of the magnetic and crystal-field properties of the hexagonal Kondo lattice YbCu3Al2, using Yb-170 Mossbauer spectroscopy in the temperature range 0.1 K-50 K. L(III)-edge x-ray absorption spectra at 10 K and 300 K were also obtained; they indicate that the Yb ion is very close to trivalent over the whole temperature range. In the antiferromagnetic phase, the thermal variation of the Yb3+ spontaneous moment has been measured and the derived transition temperature (T-N = 1.95 K) is in agreement with previous specific heat and magnetic data. In the paramagnetic phase, the two components g(z) and g(p)erpendicular to of the g-tensor of the Yb3+ ground crystal-field doublet have been measured. These g-values cannot be accounted for by a crystal-field-only model, and we interpret this in terms of a Kondo reduction of the paramagnetism (T > T-N) and of the spontaneous moment (T < T-N), with a Kondo temperature T-K similar or equal to 2.3 K. In addition, the spectra in the antiferromagnetic phase show inhomogeneous broadenings due to the presence of random distortions with respect to the hexagonal Yb site symmetry, and, close to T-N, dynamical effects are clearly evident and allow the Yb3+ fluctuation frequency to be measured in the magnetically ordered phase.