The free-boundary problem for models describing the dynamics of condensed fuel gasless combustion is studied numerically. The solution of the propagating combustion wave type is considered. The effective one-dimensional boundary problem which determines the flame wave in the framework of the model is formulated in the following way \[ {\partial \theta\over \partial \tau} - V(\tau){\partial \theta\over \partial \xi} = {\partial^ 2 \theta\over \theta\xi^ 2} + V(\tau)\delta(\xi), \;\theta(+\infty,\tau) = 0,\quad \theta(-\infty,\tau) < \infty, \] where \(\theta = \theta(\xi,\tau)\) is the dimensionless temperature and \(\xi\), \(\tau\) are the dimensionless spatial coordinate and time, respectively. The function \(V(\tau)\) is defined by \[ V(\tau) = \Omega[\theta(0,\tau)], \;\Omega = \exp(\alpha(\theta-1)/(\sigma + (1-\sigma)\theta)), \] where \(\sigma\) and \(\alpha\) (Zeldovich number) are the dimensionless parameters. The problem admits a basic state solution \[ \theta^ b = \exp(-\xi),\quad \xi > 0;\quad \theta^ b = 1,\quad \xi < 0; \quad V^ b = 1, \] corresponding to a steady planar combustion wave. This solution loses its stability at \(\alpha > \alpha_ c = 2+5^{1/2}\) by Hopf bifurcation and consequently a sequence of the period doublings which leads to a chaotic behaviour should be realized. The authors try to observe these phenomena numerically.