Fault slip occurs via earthquakes or stable creep depending on the manner in which frictional resistance varies with sliding velocity and displacement. If the form of this dependence is a function of rock type, observed spatial variations in slip behavior along faults could be explained by lithologic variation. We have used a rotary shear apparatus to investigate the frictional response of dolomite marble to changes in sliding velocity. We have modeled the results using a state variable constitutive law for rock friction and a numerical method to solve for the interaction between the friction law and the compliance of our machine. Dolomite marble displays steady state velocity strengthening, as contrasted with granite and quartzite, which show velocity weakening at the same conditions. To model the dolomite results, it is necessary to use two state variables, and surprisingly, the parameters specifying the decay magnitudes associated with these state variables differ in sign from each other. The magnitude of the parameter associated with the longer decay is negative, leading to a downward decay of frictional strength associated with a decrease in velocity. If the shorter decay is of sufficient magnitude, as we observe at low velocity, it is possible for the machine-rock system to exhibit instability and oscillatory behavior even though the steady state response is velocity strengthening. Another way in which dolomite contrasts with granite and quartzite is that the friction parameters vary strongly with velocity. A transition from unstable to stable sliding with increasing velocity has been observed previously, and our observed variation of the constitutive parameters with velocity can explain this behavior. There is some indication that the evolution of the state variables for dolomite occurs as a function of time rather than displacement, in contrast with granite and quartzite. The frictional behavior of dolomite shows that the constitutive laws that have been developed based on results from granite and quartzite are inadequate to describe all rock types and that more general laws are required.