A set-valued analogue of the classical Langevin equation on a Riemannian manifold is introduced and several existence theorems of inclusions of Langevin type are proved. Let \(v:I\to T_{m_0}M\) be a continuous curve, \({ \mathcal S}v\) the unique \(C^1\)-curve \(\gamma: I\to M\) such that \(\gamma(0) =m_0\) and \(\dot\gamma (t)\) is parallel to the vector \(v(t)\) for every \(t\in I=[0,l]\). Let \(\Gamma\alpha (t,m(t),\dot m(t))\) be the curve in \(T_{m_0}M\) such that the vector \(\Gamma\alpha (t,m(t),\dot m(t))\) is parallel to \(\alpha(t,m(t), \dot m(t))\) along \(m(\cdot)\) for every \(t\). Then the integral equation \[ m(t)={\mathcal S} \left( \int^t_0\Gamma \alpha\bigl(\tau, m(\tau),\dot m(\tau) \bigr)d \tau+C \right) \] on \(I=[0,l]\) is the integral form of the second Newton's law [\textit{Yu. E. Gliklih}, Lect. Notes Math. 1108, 128-151 (1984; Zbl 0564.70013)]. For single valued functions \(F\) and \(A\), the Langevin equation is \[ \xi(t)={\mathcal S} \left(\int^t_0 \Gamma F\bigl( \tau,\xi(t), \dot\xi (\tau)\bigr)d \tau+\int^t_0 \Gamma A\bigl( \tau,\xi (\tau),\dot \xi(\tau) \bigr)dw(\tau) +C\right). \] Let \(F\) and \(A\) be set-valued. Then the Langevin inclusion is introduced by \[ \xi(t) \in{\mathcal S}\left( \int^t_0\Gamma F\bigl(\tau, \xi(\tau), \dot\xi(\tau) \bigr)d \tau+\int^t_0 \Gamma A\bigl(\tau, \xi(\tau), \dot\xi(\tau) \bigr)dw(\tau) +C \right), \] and its weak and strong solutions are defined (Definitions 3 and 4). Several existence theorems of weak and strong solutions are proved in Sect. 3 by using \(\varepsilon\)-approximation of set-valued functions [cf. \textit{W. Kryszewski}, Homotopy properties of set-valued mappings, Toruń (1997)] and theory of stochastic processes and stochastic differential equations together with author's previous results on Langevin equation [\textit{Yu. E. Gliklikh} and \textit{I. V. Fedorenko}, On the geometrization of a certain class of mechanical systems with random perturbations of the force, Voronezh University, 1980 (in Russian), Equations of geometric mechanics with random force fields, Priblizhennye metody issledovaniya differentsial'nykh uravnenii i ikh prilozhenniya, Kuibyshev 1981, 64-72 (1981) (in Russian)).