An improved, modular convection/impingement oven assembly for continuously cooking food. In certain embodiments, the assembly comprises at least one non-recirculating impingement oven unit and at least one additional oven unit, arranged as a series, in any sequence. A first oven has an elongated chamber, a conveyer system, hot-air impingement units, and an exhaust vent at the discharge end. Preferably, it has surface-treatment burners for browning, a brander for grill marks, and/or steam nozzles for introducing heat and moisture. Cooking vapors pass the entire length of the unit. Each subsequent oven may be similar to the first oven (often omitting the surface-treatment burners and brander) with its own vent. Each subsequent oven may cook by flame, air, or steam, in any combination. Each oven unit is independently controllable for cooking parameters and cooking methods. An air gap may be provided between each pair of oven units to decouple airflow between units.