The paper presents the first algorithms for estimating non-negative Lyapunov exponents from experimental time series, which are crucial for characterizing chaotic systems. Lyapunov exponents quantify the exponential rates of divergence or convergence of nearby orbits in phase space, with positive exponents indicating chaotic behavior. The authors develop a method that monitors the long-term growth rate of small volume elements in an attractor, extending a technique previously applied to analytically defined model systems. The method is tested on model systems with known Lyapunov spectra and applied to experimental data from the Belousov-Zhabotinskii reaction and Couette-Taylor flow. The paper discusses the challenges of estimating Lyapunov exponents from noisy experimental data and provides detailed algorithms for estimating the largest and second-largest exponents, along with Fortran code for implementation. The authors emphasize the importance of choosing appropriate embedding dimensions and delay times to ensure accurate exponent estimation.The paper presents the first algorithms for estimating non-negative Lyapunov exponents from experimental time series, which are crucial for characterizing chaotic systems. Lyapunov exponents quantify the exponential rates of divergence or convergence of nearby orbits in phase space, with positive exponents indicating chaotic behavior. The authors develop a method that monitors the long-term growth rate of small volume elements in an attractor, extending a technique previously applied to analytically defined model systems. The method is tested on model systems with known Lyapunov spectra and applied to experimental data from the Belousov-Zhabotinskii reaction and Couette-Taylor flow. The paper discusses the challenges of estimating Lyapunov exponents from noisy experimental data and provides detailed algorithms for estimating the largest and second-largest exponents, along with Fortran code for implementation. The authors emphasize the importance of choosing appropriate embedding dimensions and delay times to ensure accurate exponent estimation.