This paper analyzes a two-level queuing production system with finite dedicated buffers under exponential assumptions. We consider $n$ types of arriving jobs which upon completion of service at the first-level workstation proceed to the second level and join their dedicated workstations that are laid out in parallel. Blocking occurs when the flow of job $i$ through the first-level queue is momentarily stopped owing to the capacity limitation of its second—level dedicated queue having been reached. Approximate results are derived for the blocking probabilities and the mean effective service time in the first-level workstation.