<p>In this paper, we establish oscillation conditions for a second-order neutral differential equation <Equation ID="Equ8"> <EquationSource Format="TEX">\(\begin{aligned} \big (y -py_\tau \big )''+q(t)f(y_\sigma )=0, \quad y_\delta (t) \equiv y(t-\delta ), \quad \delta \in \mathbb {R}. \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mrow> <mo maxsize="1.2em" minsize="1.2em" stretchy="true">(</mo> </mrow> <mi>y</mi> <mo>-</mo> <mi>p</mi> <msub> <mi>y</mi> <mi>τ</mi> </msub> <msup> <mrow> <mo maxsize="1.2em" minsize="1.2em" stretchy="true">)</mo> </mrow> <mrow> <mo>′</mo> <mo>′</mo> </mrow> </msup> <mo>+</mo> <mi>q</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>y</mi> <mi>σ</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mspace width="1em" /> <msub> <mi>y</mi> <mi>δ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>≡</mo> <mi>y</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>-</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>δ</mi> <mo>∈</mo> <mi mathvariant="double-struck">R</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>We prove sufficient conditions that guarantee the oscillation of solutions depending on the type of nonlinearity of the function&#xa0;<i>f</i>.</p>