GJ9827 is a bright star hosting a planetary system with three transiting planets. As a multi-planet system with planets that sprawl within the boundaries of the radius gap between terrestrial and gaseous planets, GJ9827 is an optimal target to study the evolution of the atmospheres of close-in planets with a common evolutionary history and their dependence from stellar irradiation. Here, we report on the Hubble Space Telescope (HST) and CARMENES transit observations of GJ9827 planets b and d. We performed a stellar and interstellar medium characterization from the ultraviolet HST spectra, obtaining fluxes for Ly-alpha and MgII of F(Ly-alpha) = (5.42+0.96-0.75) X 10^{-13} erg cm^{-2} s^{-1} and F(MgII) = (5.64 +- 0.24) X 10^{-14} erg cm^{-2} s^{-1}. We also investigated a possible absorption signature in Ly-alpha in the atmosphere of GJ9827b during a transit event from HST spectra, as well as H-alpha and HeI signature for the atmosphere of GJ9827b and d from CARMENES spectra. We found no evidence of an extended atmosphere in either of the planets. This result is also supported by our analytical estimations of mass-loss based on the measured radiation fields for all the three planets of this system, which led to a mass-loss rate of 0.4, 0.3, and 0.1 planetary masses per Gyr, for GJ9827b, c, and d respectively. These values indicate that the planets could have lost their volatiles quickly in their evolution and probably do not retain an atmosphere at the current stage.