We consider a process (Xt) solution of a one-dimensional nonlinear self-stabilizing stochastic differential equation, with classical drift term V (α, x) depending on an unknown parameter α, self-stabilizing term Φ(β, x) depending on another unknown parameter β and small noise amplitude ε. Self-Stabilization is the effect of including a mean-field interaction in addition to the state-dependent drift. Adding this term leads to a nonlinear or Mac Kean-Vlasov Markov process with transitions depending on the distribution of Xt. We study the probabilistic properties of (Xt) as ε tends to 0 and exhibit a Gaussian approximating process for (Xt). Next, we study the estimation of (α, β) from a continuous observation of (Xt, t ∈ [0, T ]). We build explicit estimators using an approximate log-likelihood function obtained from the exact log-likelihood function of a proxi-model. We prove that, for fixed T , as ε tends to 0, α can be consistently estimated with rate ε −1 but not β. Then, considering n i.i.d. sample paths (X i t , i = 1,. .. , n), we build consistent and asymptotically Gaussian estimators of (α, β) with rates √ nε −1 for α and √ n for β. Finally, we prove that the statistical experiments generated by (Xt) and the proxi-model are asymptotically equivalent in the sense of the Le Cam ∆-distance both for the continuous observation of one path and for n i.i.d. paths under the condition √ nε → 0, which justifies our statistical method.