We investigate a Bonhoeffer-van der Pol dynamical system with fractional derivatives of different orders. Spectral analysis is fulfilled analytically for certain relationships between derivative orders and numerically for any relation between them. It is shown that such a system could be more unstable than the system with integer derivatives even for fractional order indices less than one. Different types of oscillations appear as a result of this instability. Computer simulation of the typical oscillations demonstrating the observed effects are performed.