Summary: The goal of this article is to extend some results of I. Popescu [Probab. Theory Relat. Fields 144, No. 1–2, 179–220 (2009; Zbl 1165.82012)] in several directions. We establish the limiting spectral distribution (LSD) for \(r\)-diagonal matrices under reduced moment conditions compared to those required by Popescu [loc. cit.]. We also deal with the joint convergence of several sequences of such matrices. In particular, we show that there is a large class of such matrices where the joint limit is not free while the marginals are semicircular. We also consider matrices of the form \(X_{n}X_{n}^{T}\) where \(X _{n }\) is a sequence of nonsymmetric \(r\)-diagonal random matrices and establish their limiting spectral distribution.