We present period-luminosity (P-L) diagrams for nearby Mira and semiregular variables, selecting stars with parallaxes better than 20% and well-determined periods. Using K-band magnitudes, we find two well-defined P-L sequences, one corresponding to the standard Mira P-L relation and the second shifted to shorter periods by a factor of about 1.9. The second sequence contains only semiregular variables, while the Mira sequence contains both Mira and semiregular variables. Several semiregular stars show double periods that are in agreement with both relations. The Whitelock evolutionary track is shown to fit the data, indicating that the semiregular variables are Mira progenitors. The transition between the two sequences may correspond to a change in the pulsation mode or to a change in the stellar structure. Large-amplitude pulsations that lead to the classical Mira classification occur mainly near the tip of the local asymptotic giant branch luminosity function.