Lyapunov (Russian: Ляпунов, in old-Russian often written Лепунов) is a Russian surname that is sometimes also romanized as Ljapunov, Liapunov or Ljapunow. Notable people with the surname include:

• Alexey Lyapunov (1911–1973), Russian mathematician
• Aleksandr Lyapunov (1857–1918), son of Mikhail (1820–1868), Russian mathematician and mechanician, after whom the following are named:
  • Lyapunov dimension
  • Lyapunov equation
  • Lyapunov exponent
  • Lyapunov function
  • Lyapunov fractal
  • Lyapunov stability
  • Lyapunov's central limit theorem
  • Lyapunov time
  • Lyapunov vector
  • Lyapunov (crater)
• Boris Lyapunov (1862–1943), son of Mikhail (1820–1868), Russian expert in Slavic studies
• Mikhail Lyapunov (1820–1868), Russian astronomer
• Mikhail Nikolaevich Lyapunov (1848–1909), Russian military officer and lawyer
• Prokopy Lyapunov (d. 1611), Russian statesman
• Sergei Lyapunov (1859–1924), son of Mikhail (1820–1868), Russian composer
• Zakhary Lyapunov (d. after 1612), Russian statesman, Prokopy Lyapunov's brother