  We analyze Galactic, Large Magellanic Cloud and Small Magellanic Cloud
Cepheids and RR Lyrae variables in terms of period-color (PC) and
amplitude-color (AC) diagrams at the phases of maximum and minimum light. We
compiled Galactic Cepheids $V$- and $I$-band data from the literature. We make
use of optical bands light curve data from OGLE-III survey for Cepheids and RR
Lyrae variables in the Magellanic Clouds. We apply the $F$-statistical test to
check the significance of any variation in the slope of PC and AC relations for
Cepheid variables. The PC relation at maximum light for Galactic Cepheids with
periods longer than about 7 days is shallow and the corresponding AC relation
is flat for the entire period range. For the fundamental mode Cepheids in the
Magellanic Clouds, we find significant breaks in the PC and AC relations at
both maximum and minimum light for periods around 10 days. The PC relation at
maximum light for the Magellanic Clouds is flat for Cepheids with periods
greater than 10 days. First overtone Cepheids with periods less than 2.5 days
have a shallow PC relation at minimum light. For fundamental mode RR Lyraes, we
confirm earlier work supporting a flat PC relation at minimum light and a
significant relation between amplitude and color at maximum light. We find that
no such relations exist for first overtone RR Lyrae stars. These findings are
in agreement with stellar photosphere/hydrogen ionization front interaction
considerations. These nonlinearities can provide strong constraints for models
of stellar pulsation and evolution.
