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We are concerned vvith periodicity results for the planar delay-differential equation x(t) = -x(t) αF (x(t -1)), α > 0. With F satisfying a kind of planar negative feedback condition and some appropriate hypotheses, we state an existence theorem for nonconstant periodic solutions. Neglecting the boundedness condition on F, we show the existence of a sequence of values of α, α₀ < α₁ < ..., where a Hopf bifurcation occurs.