1. A parallel processing computer comprising: a plurality of functional units (FU.sub.1. .. FU.sub.n) for executing instructions in parallel with one another; a memory (4) for storing said instructions and data to be utilized in execution of said instructions by said functional units; a node driving register (1) for indicating instructions to be executed in parallel by said functional units, respectively; a mode register means (2) connected to said functional units for storing information indicative of either a serial and parallel operation mode of said functional units; and wherein said node driving register includes a plurality of node pointers, for serving as the program counter in a Von-Neuman processing operation, each of said node pointers (NPR) constituted by at least one word of said node driving register (1) designated by a given one of said functional units (FU.sub.1,. .. , FU.sub.n) connected with said mode register means, which is loaded with serial operation mode information and temporarily allocated for use only by said given one functional unit, to thereby serve as a program counter for a serial type operation of said given functional unit so that a serial type program is executed by said given one functional unit in cooperation with a node pointer and said memory.