  Various results and techniques, such as Bohl-Perron theorem, a priori
solution estimates, M-matrices and the matrix measure, are applied to obtain
new explicit exponential stability conditions for the system of vector
functional differential equations $$ \dot{x_i}(t)=A_i(t)x_i(h_i(t))
+\sum_{j=1}^n \sum_{k=1}^{m_{ij}} B_{ij}^k(t)x_j(h_{ij}^k(t)) +
\sum_{j=1}^n\int\limits_{g_{ij}(t)}^t K_{ij}(t,s)x_j(s)ds,~i=1,\dots,n. $$ Here
$x_i$ are unknown vector functions, $A_i, B_{ij}^k, K_{ij}$ are matrix
functions, $h_i,h_{ij}^k, g_{ij}$ are delayed arguments. Using these results,
we deduce explicit exponential stability tests for second order vector delay
differential equations.
