Nonlinear microscopy through flexible fiber-optic catheters has potential in clinical diagnostic applications. Here, we demonstrate a new approach based on wavelength-swept narrowband pulses that permits simple fiber-optic delivery without need of the dispersion management and allows nonmechanical beam scanning. Using $0.86\mathrm{ps}$ pulses rapidly tuned from $789\mathrm{nm}\text{to}822\mathrm{nm}$ at a sweep rate of $200\mathrm{Hz}$ , we demonstrate two-photon fluorescence and second-harmonic generation imaging through a $5\text{-}\mathrm{m}$ -long standard single-mode fiber.