Identity-differentiating self from external reality-and agency-being the author of one's acts-are generally considered intrinsic properties of awareness and looked at as mental constructs generated by consciousness. Here a different view is proposed. All physiological systems display complex time-dependent regulations to adapt or anticipate external changes. To interact with rapid changes, an animal needs a nervous system capable of modelling and predicting (not simply representing) it. Different algorithms must be employed to predict the momentary location of an object based on sensory information (received with a delay), or to design in advance and direct the trajectory of movement. Thus, the temporal dynamics of external events and action must be handled in differential ways, thereby generating the distinction between self and non-self ("identity") as an intrinsic computational construct in neuronal elaboration. Handling time is not what neurons are designed for. Neuronal circuits are based on parallel processing: each bit of information diverges on many neurons, each of which combines it with many other data. Spike firing reports the likelihood that the specific pattern the neuron is designed to respond to is present in the incoming data. This organization seems designed to process synchronous datasets. However, since neural networks can introduce delays in processing, time sequences can be transformed into simultaneous patterns and analysed as such. This way predictive algorithms can be implemented, and continually improved through neuronal plasticity. To successfully interact with the external reality, the nervous system must model and predict, but also differentially handle perceptual functions or motor activity, by putting in register information that becomes available at different time moments. Also, to learn through positive/negative reinforcement, modelling must establish a causal relation between motor control and its consequences: the contrast between phase lag in perception and phase lead (and control) in motor programming produces the emergence of identity (discerning self from surrounding) and agency (control on actions) as necessary computational constructs to model reality. This does not require any form of awareness. In a brain, capable of producing awareness, these constructs may evolve from mere computational requirements into mental (conscious) constructs.