Companies Helping to Find Teaching Jobs in Russia

Language Link is an English-teaching company, recognized by both the British Council and ARELS. It has worked with Central and Eastern Europe and the Far East since the early 90s. Each year Language Link, Russia, provides extensive employment opportunities for native English speakers. They enter the academic program as EFL teachers, teacher-interns, volunteers and work-study placements. The schools around Russia are numerous.

The Anglo-American School of Moscow (AAS) is a non-profit, coeducational day school for English-speaking children of American, British, and Canadian diplomats, as well as diplomats from other countries, members of the business community and Russian nationals. It is looking for enthusiastic, energetic educators. The school requires a minimum of two years' experience and certification. Tax-free starting salaries range from $25,700 to $47,700 with housing, plus a competitive benefits package for an initial two-year contract.
For further information see:

There is a company helping English-speaking volunteers to find a job abroad - Teaching and Projects abroad. There are quite a lot of possibilities, including teaching. Teaching English there means work in local schools and also work at the Moscow Continuing Education Center, teaching adults. Sometimes they work with unemployed groups at the Center to make them more employable by helping them to speak a little English.
For details, look here:

Educational Services International (ESI) appeals to serve developing countries based on Christian humanitarian principles, using education as a way of bridging diverse cultures. They train and send teachers of English, Business and Law to high schools and universities in China, Russia, Muslim Central Asia, Czech Republic, Hungary and Romania.

Eltap offers English-speakers the opportunity to assist teachers of English in high schools and post-secondary institutions in other countries. This is a low cost international experience. In Russia they have placements in Moscow, St. Petersburg and Chelyabinsk. Accommodation is with host families.
More details:

Russian and East European Institue Employment - Employment Opportunities from Indiana University.

Russian Jobs: City List - Job listings from several cities in Russia.

Seryoga's English School Find-a-Job - Job vacancies in Russia.