This paper analyzes first-order full-digital coherent and noncoherent PN code tracking loops for bandlimited baseband direct-sequence spread-spectrum signals under AWGN. The considered loop structures which employ a decimator to control the PN code phase have implementation advantages over loops employing higher-order interpolators. Analytic expressions are derived for the steady-state timing mean squared error, mean pull-in time, mean time to lose lock and the steady-state uncoded and coded bit error rates by employing appropriate Markov chain models. The analytical results are verified to be very accurate via computer simulations. Results are presented for BPSK spreading but extension to QPSK spreading is straightforward.