We use the non-stationary three dimensional two-layer outer gap model to explain gamma-ray emissions from a pulsar magnetosphere. We found out that for some pulsars like the Geminga pulsar, it was hard to explain emissions above a level of around 1 GeV. We then developed the model into a non-stationary model. In this model we assigned a power-law distribution to one or more of the spectral parameters proposed in the previous model and calculated the weighted phaseaveraged spectrum. Though this model is suitable for some pulsars, it still cannot explain the high energy emission of the Geminga pulsar. An Inverse-Compton Scattering component between the primary particles and the radio photons in the outer magnetosphere was introduced into the model, and this component produced a sufficient number of GeV photons in the spectrum of the Geminga pulsar.

In this review paper we explain the following gamma-ray emission features from the millisecond pulsars. (1) Why is the dipolar field of millisecond pulsars so weak but the magnetic pair creation process may still be able to control the size of the outergap? (2) A sub-GeV pulse component could occur in the vicinity of the radio pulse of millisecond pulsars. (3) Orbital modulated gamma-rays should exist in the black widow systems for large viewing angle.