Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)The algebra of matrices over a field has a natural -grading. Its graded identities have been described by Vasilovsky who extended a previous work of Di Vincenzo for the algebra of matrices. In this paper, we study the graded identities of block-triangular matrices with the grading inherited by the grading of . We show that its graded identities follow from the graded identities of and from its monomial identities of degree up to . In the case of blocks of sizes and 1, we give a complete description of its monomial identities and exhibit a minimal basis for its -ideal.632 302313Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [2012/16838-0]