Systems, methods, and apparatuses relating to conditional operations in a configurable spatial accelerator are described. In one embodiment, a hardware accelerator includes an output buffer of a first processing element coupled to an input buffer of a second processing element via a first data path that is to send a first dataflow token from the output buffer of the first processing element to the input buffer of the second processing element when the first dataflow token is received in the output buffer of the first processing element; an output buffer of a third processing element coupled to the input buffer of the second processing element via a second data path that is to send a second dataflow token from the output buffer of the third processing element to the input buffer of the second processing element when the second dataflow token is received in the output buffer of the third processing element; a first backpressure path from the input buffer of the second processing element to the first processing element to indicate to the first processing element when storage is not available in the input buffer of the second processing element; a second backpressure path from the input buffer of the second processing element to the third processing element to indicate to the third processing element when storage is not available in the input buffer of the second processing element; and a scheduler of the second processing element to cause storage of the first dataflow token from the first data path into the input buffer of the second processing element when both the first backpressure path indicates storage is available in the input buffer of the second processing element and a conditional token received in a conditional queue of the second processing element from another processing element is a first value.