The new model of teletraffic is proposed. This model has two components. It is shown that it is possible to select the parameters of this model in such way that the conditions of Slow Growth and Fast Growth for the first and second components hold and under some common normalization the process of aggregated traffic converges to some limit process which is the sum of Stable Levy Motion and Fractional Brownian Motion. This is some generalization of the results of Mikosch et al. ©2009 IEEE.