The effects of external optical injection taking account of polarisation and electron spin dynamics in vertical-cavity surface-emitting lasers at values of pumping close to threshold are discussed. The stability map inside and outside the locking bandwidth is given in terms of elliptical and linear polarised phenomena. Finally quasi-periodicity in terms of two carrier densities and polarised fields is discussed. 1 Introduction and Theory Optical injection in semiconductor lasers has been an interesting topic of research for over two decades [1]. Polarisation switching may have important applications in the telecommunication and electro optic fields; due to their special geometry and polarisation properties, vertical-cavity surface-emitting lasers (VCSELs) have been used for investigation of switching between the two orthogonally polarised modes [2]. Combining these two topics, our research involves spin polarised injection (SPI) in VCSELs; by using external optical injection polarised perpendicular to the lasing mode of the solitary VCSEL, and using the characteristic properties of VCSELs due to birefringence rate, γ p , and spin relaxation rate, γ s , it is possible to predict novel phenomena in the stability map of frequency detuning versus injected field. For example, compared to the conventional form of optical injection in semiconductor lasers, it has been discovered that in this model the area of chaos is reduced dramatically and replaced by quasi-stability (QS). Generally, the gain anisotropy rate, γ a , between the two orthogonal modes is much less than γ p ; in this paper we use γ a = 0. In the Spin Flip Model (SFM) [3] there are two carrier densities, the first, N, associated with the total carrier density and the second, m, as the electron spin magnetisation due to the difference between the densities of spin-up and spin-down electrons. In the SPI with low pumping values we have reported [4,5] the three linear polarisation (LP) phenomena of linear limit cycle (LLC), chaos and stability. However, the novelty of our work is more concerned with elliptical polarisation (EP) effects, namely QS, coupled limit cycle (CLC), coupled chaos (CC) and elliptical quasi-periodicity (EQP), all of which are due to the strong influence of birefringence effects.