Saturated and trans fat intake have been linked to an increased risk of developing diseases such as cardiovascular and coronary heart disease, obesity, and myocardial infarction. As a result of the actions and regulations proposed to reduce and eliminate the content of saturated and trans fats, it is necessary to develop and implement new structuring technologies, such as oleogelation. Oleogelation is a promising strategy for structuring liquid oil, that allows the incorporation of vegetable oils rich in unsaturated fatty acids into food matrix and which can provide the functionality of solid fats and improved nutritional characteristics. The partial or total replacement of conventional fats with oleogels in pastry products is of great interest due to their larger consumption. In this research paper, the puff (jam-filled puff pastry) and tender pastries (bow tie cookies, cheese crackers, apple pie, and cookies) have been reformulated by totally replacing of conventional fats with oleogel and the structural behavior in the dynamics of the technological process was evaluated. The textural properties of oleogel were comparable to those of some conventional fats, but frequency sweep measurements showed that the oleogel formulated with refined sunflower oil and carnauba wax (10% w/w) had the highest storage modulus G’ and loss modulus G’’ values when compared to conventional fats (commercial margarine, butter, a mixture of 73% margarine and 27% lard, and puff pastry margarine). The textural properties of oleogel (2.34 N and 2.30 mJ) were significantly different from those of puff pastry margarine (9.78 N and 21.73 mJ), but compared to other conventional fats, the values of hardness (1.42–2.70 N) and adhesiveness (4.40–5.17 mJ) were similar. For conventional and oleogel doughs the storage modulus (Gʹ) were higher than loss modulus (G″) and both increased with the applied frequency (Hz). In terms of the products textural profile, the prototypes formed with oleogel exhibited lower hardness values (2.37–15.64 N) than the conventional products (8.83–19.89 N), indicating the tenderizing effect produced by the oleogel. The fat losses determined during 14 days of storage showed a lower physical stability of the doughs and products formulated with oleogel, most probably due to the destabilization kinetics of the lipid system during the operations of the technological process.