Perhaps you are not using as.yearmon() correctly, because the following works for me (using dat from Gavin's answer):
library(zoo) dat$date <- as.yearmon(dat$date, "%YM%m")
Thus, while working on drawing things correctly:
Your data:
dat <- read.table(text = "date x x2 1975M1 112.44 113.12 1975M2 113.1 114.36 1975M3 115.04 114.81 1975M4 117.65 115.35 1975M5 119.5 116.92 1975M6 121.4 118.56 1975M7 120.64 118.97 1975M8 119.12 119.84 1975M9 118.91 120.59 1975M10 120.58 122.3 1975M11 121.26 123.35 1975M12 122.34 123.33", header = TRUE)
Convert to xts using as.yearmon() from the "zoo" package.
library(xts)
Building your data:
plot.zoo(dat.xts)

plot.zoo(dat.xts, plot.type="single", col = c("red", "blue"))

Update: specifying your own axes
Here are some examples of data that you can work with (itβs usually nice to share such exemplary data when asking questions about SO, as this makes it easier for others to replicate and fixes problems). Please note that in this example we skipped the use of the xts package, as it is not really needed.
set.seed(1) dat <- data.frame(date = paste0(rep(1975:1977, each = 12), "M", rep(1:12, times = 3)), x1 = runif(36, min = 100, max = 140), x2 = runif(36, min = 100, max = 140)) library(zoo)
This is the default graph obtained using plot(dat.z, screen = 1, col = 1:2) :

From your comments, it seems like you want something like monthly tags.
Build data, but suppress the x axis with xaxt = "n"
plot(dat.z, screen = 1, col = 1:2, xaxt = "n")
Make some adjustments to have a label for each month. (See ?plot.zoo where it ?plot.zoo from.)
tt <- time(dat.z)
Add your axis to your plot. It may take several experiments to find the right sizes for everything. las = 2 makes the labels perpendicular to the axis, which is required if you really feel the need to include a label for each month of each year.
axis(side = 1, at = tt[ix], labels = labs[ix], tcl = -0.7, cex.axis = 0.7, las = 2)
Here is the final plot:

By the way, if you get dates like 1977.15 , etc., you can read some answers to this question , for example, looking at using @joran pretty() .