The principle of optical trapping is conventionally based on the interaction of optical fields with linear induced polarizations. However, the optical force originating from the nonlinear polarization becomes significant when nonlinear optical nanoparticles are trapped by ultrafast laser pulses. Herein we establish the time-averaged optical forces on a nonlinear optical nanoparticle using highrepetition-rate ultrafast laser pulses, based on the linear and nonlinear polarization effects. We investigate the dependence of the optical forces on the magnitudes and signs of the refractive nonlinearities. It is found that the self-focusing effect enhances the trapping ability, whereas the selfdefocusing effect leads to the splitting of potential well at the focal plane and destabilizes the optical trap. Our results show good agreement with the reported experimental observations and provide a theoretical support for capturing nonlinear optical particles. PACS numbers: 42.65.Jx, 78.20.Bh, 78.67.Bf, 62.65.Re Optical trapping, also known as optical tweezers, is a useful technique for noncontact and noninvasive manipulation of small particles using a focused laser beam [1]. This technique has wide applications in physics, chemistry, biology, and other disciplines [2, 3]. Up to now, the stable optical trapping of micro-and nanoparticles have been extensively demonstrated by the use of continuouswave (CW) Gaussian laser beam [1-3], cylindrical vector beam [4], evanescent field [5], plasmonic field [6], spinning light fields [7], etc. Lots of efforts have been devoted to trap a variety of small objects, such as dielectric particles [1], metallic Rayleigh nanoparticles [4], semiconductor quantum dots [8], and biological cells [9].Recently, optical trapping technique has been extended by substituting CW laser with high-repetition-rate ultrafast laser pulses [10][11][12]. With the ultrafast laser pulses, several novel phenomena have been observed, including the trapping split behavior in the process of capturing gold nanoparticles by ultrafast near-infrared laser pulses [13], a controllable directional ejection of optically trapped nanoparticles [14], and the immobilization dynamics of a single polystyrene sphere [15]. It should be noted that the optical force originating from the nonlinear polarization becomes significant and cannot be neglected if the trapped particles exhibit nonlinear optical effects. Moreover, the experimental observations have revealed that the nonlinear optical effects could enhance the optical force [8,16] or modify the optical trapping potential [13].To quantitatively appraise the trapping ability, the optical force exerted on a spherical nanoparticle arising from the linear polarization has been calculated using various approaches, such as Rayleigh scattering formulae [1], Maxwell's stress tensor [17], and discrete dipole approximation [18]. For a nonlinear optical Rayleigh particle, however, the optical force unambiguously originates from the contribution of both the linear and nonlinear induced polariz...