It is vital to detect material degradation in structures early to ensure their structural safety. Nonlinear ultrasonic techniques in the guided medium are employed to interpret the material nonlinearity by quantifying the harmonic responses from the ultrasonic guided wave. In this work, we discuss the observation of a simultaneously propagating dual-mode second-harmonic (DMSH) fundamental symmetric (s0) mode and an orthogonal-shear horizontal (\mathbf{sh}-{0}^{\perp}) mode generated on a weekly nonlinear isotropic elastic plate while excited with a primary shear horizontal (SH0) mode. The presence of two dominant second harmonic modes is the reason for terming the phenomenon DMSH. Numerical simulations demonstrate the existence of dual harmonics on a thin aluminium plate. As the DMSH possesses different group velocities, each wave packet was identified in time domain analysis as separate signals. The observation is validated experimentally, and dual-mode harmonics were determined by a short-time Fourier transform (STFT) analysis of the time domain signal. A locally enhanced material nonlinearity study was conducted via numerical simulations, and the responses from DMSH were studied. It was found that the second-harmonic \mathbf{sh}-{0}^{\perp} mode was sensitive to locally enhanced material nonlinearity, while the second harmonic s0 and primary SH0 were seemingly unaffected. Improved insights from this work may provide important implications for accurate early-state defect detection in structural health monitoring and non-destructive evaluation applications of critical structures. © 2022 IEEE.