Stability of curved premixed flames in cylindrical tubes is studied in scope of the nonlinear equation derived recently in (Bychkov V.V, et al. (1999) Phys. Rev. E 60, 2897). The equation describes dynamics of a curved flame with realistic density variations across the front. It is shown that a curved flame front propagating in a tube becomes linearly unstable as soon as the tube radius exceeds certain critical value. Stability limits of curved stationary flames are investigated. Possible outcome of the obtained instability at the nonlinear stage is discussed. On the basis of the obtained results the fractal dimension of three-dimensional flames is evaluated.