The development of nonlinear fiber-endoscopes capable of imaging deeper in tissues and accessing internal organs represents a very attractive perspective for application of nonlinear optical microscopes to in-vivo research and diagnostics. The transmission of ultra-short laser pulses within a fiber is a critical issue in the development of such endoscopes. For instance, self-phase modulation (SPM), four-wave mixing (FWM) and Raman scattering occurring in conventional fibers severely affect transmitted pulses profiles in the time and frequency domains. Hollow-core (HC) fibers bring a solution to the problem, since propagation of the pulses in the air core limits nonlinear interactions. We employ here a novel double clad Kagomé-lattice HC fiber for the delivery of ultrafast pulses across a large spectral window (~400nm) with no pulse distortion. The epi-collection of the signal generated at the sample is efficiently performed with a specially designed outer multimode cladding. The fiber is incorporated in a prototype endoscope using a four-quartered piezo-electric tube to scan the laser beam on the sample. The low numerical aperture of the hollow-core (0.02) is efficiently increased by means of a dielectric microsphere attached to the fiber face. This results in tight focusing (~1 micron) of the beam at the HC fiber output. Resonant scanning of the fiber tip allows imaging over a field of 300 microns using low driving voltages. High-resolution images with different contrast mechanisms, such as SHG and TPEF, acquired with the prototype endoscope illustrate the potential of these fibers for nonlinear imaging in regions otherwise inaccessible to conventional optical microscopes.