This paper describes a new method, namely, the two-variable perturbation procedure, for the determination of acquisition times of phase-locked loops in the absence of noise. Two types of loop filters are considered : (i) perfect integrator and (ii) imperfect integrator. In both cases initial frequency deviation was assumed to be large. The results are compared with those already known in the literature. In the Case of a passive filter loop, in addition to obtaining an expression for acquisition time, the existence of limit cycles was also observed.