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For $p \in (1, \infty),$ for an integer $N \geq 2$ and for a boundedLipschitz domain $\Omega$, we consider the following nonlinear Steklovbifurcation problem \begin{equation*} \begin{aligned} -\Delta_p \phi & = 0 \;\text{in} \ \Omega, \\ |\nabla \phi|^{p-2} \frac{\partial \phi}{\partial \nu}&= \lambda \left( g |\phi|^{p-2}\phi + f r(\phi) \right) \; \text{on} \\partial \Omega, \end{aligned} \end{equation*} where $\Delta_p$ is the$p$-Laplace operator, $g,f \in L^1(\partial \Omega)$ are indefinite weightfunctions and $r \in C(\mathbb R)$ satisfies $r(0)=0$ and certain growthconditions near zero and at infinity. For $f,g$ in some appropriateLorentz-Zygmund spaces, we establish the existence of a continuum thatbifurcates from $(\lambda_1,0)$, where $\lambda_1$ is the first eigenvalue ofthe following nonlinear Steklov eigenvalue problem \begin{equation*}\begin{aligned} -\Delta_p \phi & = 0 \; \text{in} \ \Omega, \\ |\nabla\phi|^{p-2} \frac{\partial \phi}{\partial \nu} &= \lambda g |\phi|^{p-2}\phi \\text{on} \ \partial \Omega. \end{aligned} \end{equation*}

On global bifurcation for the nonlinear Steklov problems