  Let $T=(A,M,0,B)$ be a triangular matrix algebra with its corner algebras $A$
and $B$ Artinian and $_AM_B$ an $A$-$B$-bimodule. The 2-recollement structures
for singularity categories and Gorenstein defect categories over $T$ are
studied. Under mild assumptions, we provide necessary and sufficient conditions
for the existences of 2-recollements of singularity categories and Gorenstein
defect categories over $T$ relative to those of $A$ and $B$. Parts of our
results strengthen and unify the corresponding work in [27,28,34].
