The accelerator-mass-spectrometry (AMS) technique developed at the TANDAR laboratory in Buenos Aires is being mainly dedicated to environmental and astrophysical problems. For this purpose, from the earliest stages the activities have been aimed to address the upgrading and optimization of different components of the accelerator . Taking into account that only an excellent performance of the ion source and of the accelerator itself will provide reliable conditions to apply this technique, we have emphasized our work on the following areas: a) ion source and sample preparations, b) general stability and beam transmission through the accelerator, and c) detection systems. In this work we report a summary of these activities and we describe the progress achieved along all these lines. Finally, we present and discuss the initial results of the application of AMS to the measurement of the latitudinal distribution of the long-lived radioisotope ³⁶Cl in rainwater samples, and to the study of ⁵⁹Ni in meteorite material.