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Vertically stacked Josephson tunnel junctions with a high number of junctions (up to n=20) were realized using a fabrication process based on the Nb/Al technology. An experimental study aimed toward their potential applications was made. First, we report on a series of DC measurements, with the main purpose of studying the quality of the I-V curve as a function of the number of barriers in the stack; we found that the junction quality slowly becomes worse as we increase this number. In fact, some thermal effects appear, which result in an increase of the subgap current and a decrease of the width of the current jump at the total gap voltage. Further, we found a low frequency voltage noise on devices with n>10 that depends on the junction area and on the substrate nature. Later, we discuss some RF properties of stacked junctions irradiated with a microwave signal. These measurements show that they seem to behave independently. Once again, the thermal effects drastically influence the response to an external RF drive and seem to limit the use for applications of these devices.