Hi,
NDSolve[{D[u[x, t], t] == D[u[x, t], x, x] - u[x, t],
D[v[x, t], t] == D[v[x, t], x, x] - v[x, t], u[x, 0] == 1,
v[x, 0] == 1, u[0, t] == 1, Derivative[1, 0][u][1, t] == 0,
v[0, t] == u[1, t] == 1, Derivative[1, 0][v][1, t] == 0}, {u[x, t],
v[x, t]}, {x, 0, 1}, {t, 0, 5}]
works.
Cheers,
Marco
