The existence and uniqueness of solutions and a representation of solution formulas are studied for the following initial value problem: x ˙ ( t ) + ∫ t 0 t K ( t , s ) x ( h ( s ) ) d s = f ( t ) ,   t ≥ t 0 ,   x ∈ ℝ n , x ( t ) = φ ( t ) , t < t 0 . Such problems are obtained by transforming second-order delay differential equations x ¨ ( t ) + a ( t ) x ˙ ( g ( t ) ) + b ( t ) x ( h ( t ) ) = 0 to first-order differential equations.