Abstract. We examine the dynamical behaviour of the phenomenological Burridge–Knopoff-like model with one and two blocks, where the friction term is supplemented by the time delay τ and the variable friction strength c. Time delay is assumed to reflect the initial quiescent period of the fault healing, considered to be a function of history of sliding. Friction strength parameter is proposed to mimic the impact of fault gouge thickness on the rock friction. For the single-block model, interplay of the introduced parameters c and τ is found to give rise to oscillation death, which corresponds to aseismic creeping along the fault. In the case of two blocks, the action of c₁, c₂, τ₁ and τ₁ may result in several effects. If both blocks exhibit oscillatory motion without the included time delay and frictional strength parameter, the model undergoes transition to quasiperiodic motion if only c₁ and c₂ are introduced. The same type of behaviour is observed when τ₁ and τ₂ are varied under the condition c₁ = c₂. However, if c₁, and τ₁ are fixed such that the given block would lie at the equilibrium while c₂ and τ₂ are varied, the (c₂, τ₂) domains supporting quasiperiodic motion are interspersed with multiple domains admitting the stationary solution. On the other hand, if (c₁, τ₁) warrant oscillatory behaviour of one block, under variation of c₂ and τ₂ the system's dynamics is predominantly quasiperiodic, with only small pockets of (c₂, τ₂) parameter space admitting the periodic motion or equilibrium state. For this setup, one may also find a transient chaos-like behaviour, a point corroborated by the positive value of the maximal Lyapunov exponent for the corresponding time series.