The condensed phase of fatty acid ethyl ester monolayers exhibits long range orientational order. The aliphatic chains are only weakly tilted in these monolayers. This has an effect on the textures of the monolayers. The domains of the condensed phase formed during a transition from the fluid phase to a condensed phase with tilted chains do not have a defined substructure. Different types of domain substructures can be observed. A few domains have a segment structure with chains tilted perpendicular to the bisector of the segment. Other domains of the same monolayer have small parts of a deviating orientation embedded in the major part of the domain having an uniform orientation. Using domains with this texture, the anisotropy of the line tension is qualitatively estimated. Jumps of the molecular orientation occur along various dense lattice directions, which corresponds to the observation of up to four main growth directions in the dendritic growth regime of ethyl stearate monolayers, However the large spread of textures is not only introduced by the dendritic growth. This becomes evident from the study of the ethyl palmitate monolayers, where no dendritic growth regime exists. Also in these monolayers various structures occur : some of them are identical to those of the ethyl stearate monolayers.