In this paper, we study the stability under direct sums and restrictions of some strong variations of Weyl and Browder type theorems recently introduced in Rashid and Prasad (Asia-Eur J Math 8:14, 2015. https://doi.org/10.1142/S1793557115500126), Sanabria et al. (Rev Colomb Mat 51(2):153–171, 2017a, Acta Math Univ Comen (NS) 86(2):345–356, 2017b, Open Math 16(1):289–297, 2018).En este documento, estudiamos la estabilidad bajo sumas y restricciones directas de algunas variaciones importantes de los teoremas de tipo Weyl y Browder recientemente introducidos en Rashid y Prasad (Asia-Eur J Math 8:14, 2015. https://doi.org/10.1142 / S1793557115500126), Sanabria et al. (Rev Colomb Mat 51 (2): 153–171, 2017a, Acta Math Univ Comen (NS) 86 (2): 345–...