This paper presents an adaptive control scheme for first-order systems of the form y + a*y = b0*u + b1*u which may possibly be a nonminimum phase. The control scheme achieves asymptotical stabilization without any a priori knowledge on the plant parameters. The adaptive scheme is free from singularities in the sense that the plant estimated model is always controllable. The singularity has been overcome through a suitable modification of the parameter estimates, which is based on standard least squares covariance matrix properties, and the use of a hysteresis switching function.