We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form ( x ( t ) + x ( t − 1 ) ) ′′ = q x ( 2 [ ( t + 1 ) / 2 ] ) + f ( t ) , where [ ⋅ ] denotes the greatest integer function, q is a real nonzero constant, and f ( t ) is almost periodic.