We develop oscillatory results for the n-th order (n\(\geq 1)\) differential equations of the retarded \[ y^{(n)}(t)+(- 1)^{n+1}\sum^{k}_{i=1}p_ i^ ny(t-n\tau_ i)=0 \] and the advanced type \[ y^{(n)}(t)-\sum^{\ell}_{j=1}q_ j^ ny(t+n\sigma_ j)=0 \] where \(p_ i,\tau_ i\), \(i=1,2,...,k\) and \(q_ j\), \(\sigma_ j,j=1,2,...,\ell\) are positive constants, and then we combine them to obtain oscillation results for all solutions of the differential equations of mixed type \[ (*)\quad y^{(n)}(t)- \sum^{k}_{i=1}p_ i^ ny(t-n\tau_ i)-\sum^{\ell}_{j=1}q_ j^ ny(t+n\sigma_ j)=0 \] and \[ (**)\quad y^{(n)}(t)+\sum^{k}_{i=1}p_ i^ ny(t-n\tau_ i)+\sum^{\ell}_{j=1}q_ j^ ny(t+n\sigma_ j)=0. \]