Disclosed is a process for producing unsaturated aldehydes and/or unsaturated acids from olefins or alkanes in a fixed bed shell-and-tube heat exchanger-type reactor by catalytic vapor phase oxidation. A heat exchanger-type reactor for use in such a process is also disclosed. In the process, at least one of the first-step reaction zone and the second-step reaction zone is divided into two or more shell spaces by at least one partition; each of the divided shell spaces is independently heat-controlled; a heat transfer medium in the first shell space of the first-step reaction zone or the first shell space of the second-step reaction zone has a temperature ranging from the lowest active temperature of a catalyst layer packed in a reaction tube corresponding to the first shell space of the first-step reaction zone or the first shell space of the second-step reaction zone to [the lowest active temperature + 20 °C], when referring to the two or more shell spaces corresponding to the first-step reaction zone sequentially as the first shell space of the first-step reaction zone, the second shell space of the first-step reaction zone, ..., the nth shell space of the first-step reaction zone, and the two or more shell spaces corresponding to the second-step reaction zone sequentially as the first shell space of the second-step reaction zone, the second shell space of the second-step reaction zone, ... , the nth shell space of the second-step reaction zone; and the first shell space of the first-step reaction zone or the first shell space of the second-step reaction zone is controlled in such a manner that the first shell space provides a reactant conversion contribution per length as defined in Equation 1 or 2 of 1.2∼2.5.