  The first two years of COBE DMR observations of the CMB anisotropy are
analyzed and compared with our previously published first year results. The
results are consistent, but the addition of the second year of data increases
the precision and accuracy of the detected CMB temperature fluctuations. The
two-year 53 GHz data are characterized by RMS temperature fluctuations of
DT=44+/-7 uK at 7 degrees and DT=30.5+/-2.7 uK at 10 degrees angular
resolution. The 53X90 GHz cross-correlation amplitude at zero lag is
C(0)^{1/2}=36+/-5 uK (68%CL) for the unsmoothed 7 degree DMR data. A likelihood
analysis of the cross correlation function, including the quadrupole
anisotropy, gives a most likely quadrupole-normalized amplitude
Q_{rms-PS}=12.4^{+5.2}_{-3.3} uK (68% CL) and a spectral index
n=1.59^{+0.49}_{-0.55} for a power law model of initial density fluctuations,
P(k)~k^n. With n fixed to 1.0 the most likely amplitude is 17.4 +/-1.5 uK (68%
CL). Excluding the quadrupole anisotropy we find Q_{rms-PS}= 16.0^{+7.5}_{-5.2}
uK (68% CL), n=1.21^{+0.60}_{-0.55}, and, with n fixed to 1.0 the most likely
amplitude is 18.2+/-1.6 uK (68% CL). Monte Carlo simulations indicate that
these derived estimates of n may be biased by ~+0.3 (with the observed low
value of the quadrupole included in the analysis) and {}~+0.1 (with the
quadrupole excluded). Thus the most likely bias-corrected estimate of n is
between 1.1 and 1.3. Our best estimate of the dipole from the two-year DMR data
is 3.363+/-0.024 mK towards Galactic coordinates (l,b)= (264.4+/-0.2 degrees,
+48.1+/-0.4 degrees), and our best estimate of the RMS quadrupole amplitude in
our sky is 6+/-3 uK.
