In this paper, we investigate the admissible entire solutions of finite order of the differential-difference equations (f′(z))2+P2(z)f2(z+c)=Q(z)eα(z)\documentclass[12pt]{minimal}
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\begin{document}$(f'(z))^{2}+P^{2}(z)f^{2}(z+c)=Q(z)e^{\alpha(z)}$\end{document} and (f′(z))2+[f(z+c)−f(z)]2=Q(z)eα(z)\documentclass[12pt]{minimal}
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\begin{document}$(f'(z))^{2}+[f(z+c)-f(z)]^{2}=Q(z)e^{\alpha(z)}$\end{document}, where P(z)\documentclass[12pt]{minimal}
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\begin{document}$P(z)$\end{document}, Q(z)\documentclass[12pt]{minimal}
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\begin{document}$Q(z)$\end{document} are two non-zero polynomials, α(z)\documentclass[12pt]{minimal}
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\begin{document}$\alpha(z)$\end{document} is a polynomial and c∈C∖{0}\documentclass[12pt]{minimal}
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\begin{document}$c\in\mathbb{C}\backslash\{0\}$\end{document}. In addition, we investigate the non-existence of entire solutions of finite order of the differential-difference equation (f′(z))n+P(z)fm(z+c)=Q(z)\documentclass[12pt]{minimal}
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\begin{document}$(f'(z))^{n}+P(z)f^{m}(z+c)=Q(z)$\end{document}, where P(z)\documentclass[12pt]{minimal}
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\begin{document}$P(z)$\end{document}, Q(z)\documentclass[12pt]{minimal}
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\begin{document}$Q(z)$\end{document} are two non-constant polynomials, c∈C∖{0}\documentclass[12pt]{minimal}
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\begin{document}$c\in\mathbb{C}\backslash\{0\}$\end{document}, m, n are positive integers and satisfy 1m+1n<2\documentclass[12pt]{minimal}
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\begin{document}$\frac{1}{m}+\frac{1}{n}<2$\end{document} except for m=1\documentclass[12pt]{minimal}
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\begin{document}$m=1$\end{document}, n=2\documentclass[12pt]{minimal}
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\begin{document}$n=2$\end{document}.
