This paper presents the selection of the most acceptable combination of exterior building design and thermal engineering system for a family house in Pula that meets the criteria for near zero energy consumption. The annual primary energy required for such a house must be less than 35 kWh/m2a (for littoral Croatia) and at least 30% of it must come from renewable energy sources. For that purpose calculations for heat loss, thermal loads and necessary annual energy for heating, cooling and preparation of DHW were made for this object. These results served as a base for the creation of three differents variants of the system which include: - Variant I: boiler for heating and if necessary preparation of DHW on pellets whose nominal heat output is 14 kW in a combination with floor heating, collector system and a multi-split cooling system with a capacity of 10 kW - Variant II: condensing boiler for heating and if necessary preparation of DHW on natural gas whose nominal heat output is 17,8 kW in a combination with floor heating, collector and photovoltaic system and a multi-split cooling system with a capacity of 10 kW - Variant III: air-to-water heat pump in a combination with fan coils for heating, cooling and the preparation of DHW with a nominal heat output of 11,20 kW and cooling capacity of 12,1 kW and a photovoltaic system. For each of the variants, a second part of the budget was created.That part includes the calculation of annual delivered energy (Edel, kWh) and primary energy (Eprim, kWh). Except that investment, operation and maintenance costs were also analyzed for a period of 15 years. Ultimately, „Variant II“ turned out to be the most acceptable variant of the system.