The classical DNA aptamer for adenosine and ATP was selected twice using ATP as the target in 1995 and 2005, respectively. In 2022, this motif appeared four more times from selections using adenosine, ATP, theophylline, and caffeine as targets, suggesting that this aptamer can also bind methylxanthines. In this work, using thioflavin T fluorescence spectroscopy, this classical DNA aptamer showed Kd values for adenosine, theophylline, and caffeine of 9.5, 101, and 131 μM, respectively, and similar Kd values were obtained using isothermal titration calorimetry. Binding to the methylxanthines was also observed for the newly selected Ade1301 aptamer but not for the Ade1304 aptamer. The RNA aptamer for ATP also had no binding to the methylxanthines. Molecular dynamics simulations were performed using the classical DNA and RNA aptamers based on their NMR structures, and the simulation results were consistent with the experimental observations, explaining the selectivity profiles. This study suggests that a broader range of target analogues need to be tested for aptamers. For the detection of adenosine and ATP, the Ade1304 aptamer is a better choice due to its better selectivity.