We obtain conditions for existence and (almost) non-oscillation of solutions of a second order linear homogeneous functional differential equations u ′′(x) +∑ i pi(x)u ′ (hi(x)) +∑ i qi(x)u(gi(x)) = 0 without the delay conditions hi(x), gi(x) ≤ x, i = 1, 2, . . ., and u ′′(x) + ∫ ∞ 0 u ′ (s)dsr1(x, s) + ∫ ∞ 0 u(s)dsr0(x, s) = 0.